Significance.

The altar reflects the Augustan vision of Roman civil religion. The lower register of its frieze depicts vegetal work meant to communicate the abundance and prosperity of the Roman Peace (), while the monument as a whole serves a civic ritual function whilst simultaneously operating as propaganda for Augustus and his regime, easing notions of autocracy and dynastic succession that might otherwise be unpalatable to traditional Roman culture.

Structure.

The monument consists of a traditional open-air altar at its centre surrounded by precinct walls which are pierced on the eastern and western ends (so called today because of the modern layout) by openings and elaborately and finely sculpted entirely in Luna marble.

The altar.

Within the enclosing precinct walls, the altar itself was carved with images illustrating the "lex aria", the law governing the ritual performed at the altar. The sacrificial procession depicts animals being led to sacrifice by figures carved in a Republican style similar to the so-called "Altar of Domitius Ahenobarbus", in sharp contrast with the style on the exterior of the precinct walls. What remains of the altar is otherwise fragmentary, but it appears to have been largely functional with less emphasis on art and decoration.  The interior of the precinct walls are carved with bucrania, ox skulls, from which carved garlands hang. The garlands bear fruits from various types of plants, all displayed on a single garland as allegorical representations of plenty and abundance. The bucrania in turn evoke the idea of sacrificial piety, appropriate motifs for the interior of the altar precinct. The lower register of the interior walls imitate the appearance of traditionally wooden altar precincts, which were meant to bring to mind other such altars in Rome and the tradition of constructing altars at the boundary of the city's "pomerium."

Exterior wall decoration.

The exterior walls of the Ara Pacis are divided between allegorical and pseudo-historical relief panels on the upper register while the lower register comprises scenes of nature: harmonic, intertwined vines that contain wildlife and connote nature under control. The upper register of the northern and southern walls depict scenes of the emperor, his family, and members of the regime in the act of processing to or performing a sacrifice. Various figures in togas are shown with their heads covered ("capite velato"), signifying their role as both priests and sacrificiants. Other figures wear laurel crowns, traditional Roman symbols of victory. Members of individual priestly colleges are depicted in traditional garb appropriate to their office, while lictors can be identified by their iconographic "fasces". Women and children are also included among the procession; the depiction of children in Roman sculpture would have been novel at the time of the Altar's construction, evoking themes of moral and familial piety, as well as easing concerns over dynastic intentions while simultaneously introducing potential heirs to the public eye.  The western and eastern walls are both pierced by entryways to the altar, although the interior would only have been accessed by a stairway on the western side. The entryways were flanked by panels depicting allegorical or mythological scenes evocative of peace, piety and tradition. On the eastern wall, panels depicted the seated figures of Roma and Pax, while the western side depicts the discovery of the twins and she-wolf and the sacrifice of a figure traditionally identified as Aeneas, but increasingly believed to be Rome's second king, Numa Pompilius. The identity of these various figures has been a point of some controversy over the years, relying heavily on interpretation of fragmentary remains, discussed below.  The sculpture of the Ara Pacis is primarily symbolic rather than decorative, and its iconography has several levels of significance. Studies of the Ara Pacis and similar public Roman monuments traditionally address the potent political symbolism of their decorative programs, and their emphasis and promulgation of dynastic and other imperial policies; they are usually studied as a form of imperial propaganda. The Ara Pacis is seen to embody without conscious effort the deep-rooted ideological connections among cosmic sovereignty, military force, and fertility that were first outlined by Georges Dumézil, connections which are attested in early Roman culture and more broadly in the substructure of Indo-European culture at large. Peter Holliday suggested that the Altar's imagery of the Golden Age, usually discussed as mere poetic allusion, appealed to a significant component of the Roman populace. The program of the Ara Pacis addressed this group's very real fears of cyclical history, and promised that the rule of Augustus would avert the cataclysmic destruction of the world predicted by contemporary models of historical thought.

The east and west walls.

The East and West walls each contain two panels, one well preserved and one represented only in fragments.  The East Wall contains a badly preserved scene of a female warrior ("bellatrix"), possibly Roma, apparently sitting on a pile of weapons confiscated from the enemy, thus forcing peace upon them by rendering them unable to make war. This scene has been reconstructed, based on coins that depict such a seated Roma. When the monument was being reconstructed at its present site, Edmund Buchner and other scholars sketched what the panel may have looked like. This interpretation, although widely accepted, can not be proved correct, as so little of the original panel survives.  The other panel is more controversial in its subject, but far better preserved. A goddess sits amid a scene of fertility and prosperity with twins on her lap. Scholars have variously suggested that the goddess is Italia, Tellus (Earth), Venus, and Peace, although other views also circulate. Due to the widespread depiction around the sculpture of scenes of peace, and because the Altar is named for "peace", the favoured conclusion is that the goddess is Pax.  The West Wall also contains two panels. The fragmentary "Lupercal Panel" apparently preserves the moment when Romulus and Remus were discovered by Faustulus the shepherd, while Mars looks on. Again this panel is a modern drawing without much evidence. Marble fragments of the tree and the head and shoulder of Mars (if it is Mars) and part of a second individual (thought to be Faustulus) survive, but the addition of the she-wolf, Romulus, and Remus is entirely speculative.  The better preserved scene depicts the sacrifice of a pig (the standard sacrifice when Romans made a peace treaty) by an old priest and two attendants. In 1907, this scene was identified by Johannes Sieveking as the moment when Aeneas, newly arrived in Italy, sacrificed a sow and her 30 piglets to Juno, as told by Virgil and others, even though the scene differs greatly from Vergil's description. In the 1960s, Stephan Weinstock challenged this identification (and the very identity of the entire monument), citing numerous discrepancies that Sieveking and his followers had failed to notice between Vergil's version and the panel. Subsequently, the suggestion was made that the scene shows Numa Pompilius, the Roman king associated with Peace and the Gates of Janus. Paul Rehak later published an article with this proposal, confirmed in a chapter of his posthumous book. This theory has won over many scholars, despite considerable initial resistance.

The figures.

The long friezes of the Ara Pacis (the North and South Walls) contain figures advancing towards the West, who participate in a state of thanksgiving to celebrate the Peace created by Augustus. These figures fall into four categories: lictors (men carrying fasces, bodyguards of magistrates); priests (three of the four major "collegia" – "Pontifices", "Septemviri", and "Quindecimviri"): women and children (generally from the imperial family, represented in portraiture); and attendants (a few anonymous figures necessary for religious purposes).  In addition there are two or three non-Roman children, who may be guests (or hostages) in Rome. Their identification by their non-Roman costume and their participation in the ceremony advertises to all that Rome is the centre of the world, and that other nations send their young to Rome to learn Roman ways, so great is Rome's reputation. The ceremony took place in the summer of 13 BC, but not necessarily on 4 July, when the Senate voted to build the Ara Pacis.

North wall.

The north wall has about 46 extant or partially extant figures. The first two foreground figures are lictors, carrying fasces (bundles of rods symbolizing Roman authority). The next set of figures consists of priests from the college of the Septemviri epulones, so identified by an incense box they carry with special symbols. One member of this college is missing in a gap.  After them follows the "collegium" of the "quindecimviri sacris faciundis", also identified by the incense box carried by a public slave among them. Although the name suggests this college has exactly fifteen members, the size of the college has grown to 23, including Augustus and Agrippa, who appear on the South Frieze. The other twenty-one members are present here. Two very badly damaged figures in the middle are split by a gap. From photos, the gap appears to affect a single figure, but as Koeppel, Conlin, and Stern have proven, in-site examination reveals that one is a foreground and the other a background figure.  The last portion of the North Frieze consists of members of the imperial family. Many scholars used to identify the veiled, leading figure as Julia, daughter of Augustus, but since Julia appears on the South Frieze, it is more likely that this figure is Octavia Minor. Other figures in the entourage might include Marcella Major (a daughter of Octavia), Iullus Antonius (a son of Mark Antony), and two boys and a girl of the imperial family.  In 1894, and again in 1902 and 1903, Eugen Petersen suggested that Lucius Caesar appears with Agrippa, dressed in a "Trojan" costume for the Troy Game held in 13 BC (see below). Many scholars, realizing by 1935 that Lucius was too young to be the boy beside Agrippa, preferred to identify him as Gaius. They named the smallest child on the North Frieze "Lucius," even though he is a mere toddler (Lucius was four in 13 BC). Some scholars assumed this boy also was a participant in the Troy Games, although he is certainly too young (six or seven was the minimum age). If this toddler were Lucius, he would be too young and in the wrong costume for the Troy Games. The best guess is that he is a Germanic tribal prince, but he is certainly not a dressed as a Trojan. As Charles Brian Rose has noted, "The variable value of the Eastern costume and the uneasy interaction of Trojan and Parthian iconography can make it difficult to determine whether one is viewing the founders of the Romans or their fiercest opponents."  The youth wearing Hellenistic Greek clothing suited to a Hellenistic prince has been identified as Gaius in the guise of a "camillus", an adolescent attendant of the Flamen Dialis. The Gaius identification is best supported by his size, however an additional boy in Roman dress who has a "bulla" (but has lost his head!) is also the right size, and therefore a better guess. For Gaius to appear in public without his "bulla" would invite the evil eye. This same figure in Hellenistic dress has also been interpreted as Ptolemy of Mauretania representing Africa, along with the German boy (Europe) and the Parthian prince (Asia). A foreign prince would not wear a "bulla".

South wall.

The South Wall has seen a great deal of scholarship and the greatest number of academic debates. Unlike the North Wall, where most of the heads are new (not authentic ancient heads, but modern creations), the heads of the figures on the South Wall are mostly original. Some half dozen figures are recognizable from looking at other surviving statues of members of the imperial family. Nevertheless, much debate has taken place over many of these figures, including Augustus, Agrippa, Tiberius, Julia, and Antonia.  The figure of Augustus was not discovered until the 1903 excavation, and his head was damaged by the cornerstone of the Renaissance palazzo built on top of the original Ara Pacis site. Although he was identified correctly in 1903, Petersen, Strong, and Stuart-Jones initially saw the figure as the "rex sacrorum". Today Augustus is better recognized by his hair style than his face.  In the absence of Augustus from the panel, early scholars debated whether Agrippa (the tall veiled priest) was Augustus or Agrippa or Lepidus. In 1907, Sieveking proposed that this figure was Lepidus, the "Pontifex Maximus" in 13 BC. Sieveking later reversed his position with a series of peculiar suggestions. In 1926, Loewy compared the Ara Pacis Agrippa to the Louvre Agrippa and the Agrippa in Copenhagen (and elsewhere) in order to demonstrate the iconographical similarity. Aside from a very small minority of scholars (most vehemently defensive of Lepidus in "Rom. Mitt" in the 1930s was Ludwig Curtius), the rest of the academy concluded that this figure is Agrippa. Ryberg's 1949 article gave further weight to that conclusion.  Many scholars continue to see the Julia figure as Livia, having reasoned that Livia has to be on the Ara Pacis. Indeed, Livia does appear somewhere (her exclusion is unlikely), but by 13 BC Julia had politically eclipsed Livia, as has been understood and explained by many scholars. The identification dates back to Milani in 1891. Furthermore, Livia has no bond to Agrippa, whereas Julia was his wife and expected to be the unofficial empress of Rome for decades, during and beyond Augustus' lifetime. Julia also better personified Augustus' new pro-natalism program, having already given birth to four surviving children (and was pregnant with a fifth). Surprisingly, a majority of scholars in 2000 preferred to see this figure as Livia.  The Tiberius figure was identified as such by Milani, an identification that was rarely questioned until the 1940s. Moretti, in making the glass museum for the Ara Pacis at Mussolini's command, guessed that the two consuls (Tiberius and Varus) of 13 flank Augustus, so he saw this figure as M. Valerius Messalla. V. H. von Poulsen and Toynbee proposed Iullus Antonius. But as has been well established, Augustus is flanked by priests, and this figure is Tiberius. Boschung and Bonanno have both matched the face to early period Tiberius statuary.  In relation to Antonia, Drusus, and Germanicus, H. Dütschke proposed in 1880 the correct identity for Antonia and Drusus, but incorrectly saw the toddler as Claudius. A. von Domaszewski amended this family identification and correctly saw the child as Germanicus. He also suggested that the Ara Pacis is arranged in family groups. He correctly determined that the two-year-old child could be only Germanicus, whose exact birth on 24 May 15 BC is known. This helps prove that the ceremony is an event in 13, although a few scholars continued to argue the ceremony was that of 9 BC (until definitive proof in favor of 13 came out in 1939).  In relation to the Domitii Ahenobarbi, von Domaszewski also proposed in the same 1903 article that the last family on the South Wall is that of the father of the emperor Nero (born Lucius Domitius Ahenobarbus). This identification remains widespread today. Pollini provides the best summary of this viewpoint in his article, "Ahenobarbi, Appuleii and Some Others on the Ara Pacis", where he points out that the writer Suetonius specifically mentions that Nero's father went "to the East on the staff of the young Gaius Caesar". As this campaign is known to have begun in 2 BC, it means that Gnaeus must have been of mature age by that time, therefore requiring a birth year of at least 17 BC, which would, in turn, make him sufficiently old to be the boy on the Ara Pacis. Pollini also reasons that the delay in Gnaeus' career (only reaching the consulship in 32 AD) resulted from his documented unpleasant character and points out that the careers of other members of the family with undesirable traits also suffered similar delays, notably Augustus' youngest grandson, Agrippa Postumus, who had no career, and Germanicus' brother, the later emperor, Claudius, whose career started late. However, there are some dissenters from this theory. Stern claims that these figures cannot possibly be the Domitii Ahenobarbi, on the basis of the belief that Gnaeus Domitius Ahenobarbus, whom von Domaszewski saw as the boy of the family, was born after the monument's completion. Syme had also argued that Gnaeus was born after the monument's completion, but accepted the identification of the Ahenobarbus family, preferring to identify the boy as an otherwise unknown elder brother and the girl figure as an otherwise unknown elder sister of Gnaeus—both of whom died young. Syme also proved somewhat unintentionally, based on the inscription "ILS" 6095 that Lucius Domitius Ahenobarbus was governor of Africa in 13 BC and could not be in Rome for the Ara Pacis ceremony.  Starting in 1894, Eugen Petersen suggested that Lucius Caesar appears between Augustus (this veiled figure is actually Agrippa) and Livia (actually Julia). Petersen had a good about families grouping together, but he identified none of the figures correctly in this place. In the 1920s as more and more scholars decided the scene dates to 13 BC, Loewy proposed that Lucius was too young to be this boy. After Loewy's 1926 article, consensus shifted to Gaius Caesar. Gaius, seven years old in 13 BC, fit better. Moretti canonized that Gaius was dressed in a "Trojan" costume for the equestrian boys event called the Troy Game, which was held in 13 or possibly 11 BC for the dedication of the Theater of Marcellus. This theory won universal acceptance for many decades, even though the evidence is overwhelmingly against. The boy is clearly not a Roman, given his clothing, lack of "bulla", and hair style. So ingrained was Petersen's theory, however, that when the distinguished scholar Erika Simon (1968, 18) suggested the boy is a barbarian, she was subjected to intense criticism until she retracted. Subsequently, led by Charles Brian Rose and Ann Kuttner, North American scholars have realized Petersen was wrong: the boy is a foreign prince. Stern adds the costume is wrong for a Trojan (no Phrygian hat) and no "bulla" – worn by all Roman boys as protection from the evil eye. Many others have contributed to disprove Petersen's theory.

Excavation and conservation.

The first protective building housing the monument by architect Morpurgo.

In 1938 the finally reconstructed Ara was placed near the Mausoleum of Augustus, and a big pavilion was built around it by architect Vittorio Ballio Morpurgo as part of Benito Mussolini's attempt to create an ancient Roman "theme park" to glorify Fascist Italy. Several dozens of the buildings surrounding the Mausoleum were levelled to free up space around the monument. This led to a great number of complaints from locals, starting a long series of arguments and criticisms of the Ara Pacis project. These arguments are ongoing despite having the original pavilion replaced by a new one in 2006, known as "Ara Pacis museum".

The new protective building housing the monument by architect Meier.

The historic Fascist style building around the Altar, locally known as "teca del Morpurgo", was pulled down in 2006, and replaced by a glass and steel structure in modern style, designed by architect Richard Meier. The new cover building, which has been named "Ara Pacis museum", now stands on the same site as Mussolini's structure. This new structure is much bigger than the previous one and it is divided in multiple rooms and sections besides the main one containing the altar.  Meier's building construction caused new arguments and criticism, after the ones which accompanied the first building construction, both from Rome inhabitants and foreign observers, probably due both to political memory tied to the pre-existent pavilion and to the visual impact of the new pavilion, which in the opinion of many is in stark contrast with surrounding historical buildings.  Nicolai Ouroussoff, of "The New York Times" called the building "a contemporary expression of what can happen when an architect fetishizes his own style out of a sense of self-aggrandizement. Absurdly over-scale, it seems indifferent to the naked beauty of the dense and richly textured city around it." Former mayor Gianni Alemanno, backed in July 2008 by culture undersecretary Francesco Maria Giro, pledged to tear down the new structure. He later changed his stance on the building and has agreed with Mr. Meier to modifications including drastically reducing the height of the wall between an open-air space outside the museum and a busy road along the Tiber river. The city plans to build a wide pedestrian area along the river and run the road underneath it. "It's an improvement," says Meier, adding that "the reason that wall was there has to do with traffic and noise. Once that is eliminated, the idea of opening the piazza to the river is a good one." The mayor's office said Alemanno hopes to complete the project before the end of his term in 2013.

The Ara Pacis Augustae (Latin, "Altar of Augustan Peace"; commonly shortened to Ara Pacis) is an altar in Rome dedicated to Pax, the Roman goddess of Peace. The monument was commissioned by the Roman Senate on July 4, 13 BC to honour the return of Augustus to Rome after three years in Hispania and Gaul and consecrated on January 30, 9 BC. Originally located on the northern outskirts of Rome, a Roman mile from the boundary of the "pomerium" on the west side of the Via Flaminia, the Ara Pacis stood in the northeastern corner of the Campus Martius, the former flood plain of the Tiber River and gradually became buried under of silt deposits. It was reassembled in its current location, now the Museum of the Ara Pacis, in 1938, turned 90° from its original orientation so that the original western side now faces south.

和平祭坛(拉丁语:Ara Pacis Augustae)是一个供奉和平女神的祭坛,公元前13年7月4日由罗马元老院修建,以庆祝罗马皇帝奥古斯都从西班牙和高卢凯旋,公元前9年1月30日罗马元老院进行祝圣,以庆祝奥古斯都胜利后为帝国带来的和平。它试图描绘罗马和平时期的和平与繁荣,并提醒人们,这些是因朱里亚·克劳狄王朝带来的罗马帝国的军事优势而有的。


Operations.

The Moscow Metro, a state-owned enterprise, is long and consists of twelve lines and 223 stations organized in a spoke-hub distribution paradigm, with the majority of rail lines running radially from the centre of Moscow to the outlying areas. The Koltsevaya Line (line 5) forms a long circle which enables passenger travel between these diameters, and the new Moscow Central Circle (line 14) forms a longer circle that serves a similar purpose on middle periphery. Most stations and lines are underground, but some lines have at-grade and elevated sections; the Filyovskaya Line, Butovskaya Line and the Central Circle Line are the three lines that are at grade or mostly at grade.  The Moscow Metro uses the

Stations.

Of the metro's 232 stations, 88 are deep underground, 123 are shallow, 12 are surface-level and 5 are elevated.  The deep stations comprise 55 triple-vaulted pylon stations, 19 triple-vaulted column stations, and one single-vault station. The shallow stations comprise 79 spanned column stations (a large portion of them following the "centipede" design), 33 single-vaulted stations (Kharkov technology), and three single-spanned stations. In addition, there are 12 ground-level stations, four elevated stations, and one station

Lines.

Each line is identified by a name, an alphanumeric index (usually consisting of just a number) and a colour. The colour assigned to each line for display on maps and signs is its colloquial identifier, except for the nondescript greens and blues assigned to the Kakhovskaya, the Zamoskvoretskaya, the Lyublinsko-Dmitrovskaya, and Butovskaya lines (route 11, 2, 10, and 12). The upcoming station is announced by a male voice on

Rolling stock.

Since the beginning, platforms have been at least long to accommodate eight-car trains. The only exceptions are on the Filyovskaya Line: Vystavochnaya, Mezhdunarodnaya, Studencheskaya, Kutuzovskaya, Fili, Bagrationovskaya, Filyovsky Park and Pionerskaya, which only allows six-car trains (note that this list includes all ground-level stations on the line, except Kuntsevskaya, which allows normal length trains).  Trains on the Zamoskvoretskaya, Kaluzhsko-Rizhskaya, Tagansko-Krasnopresnenskaya, Kalininskaya, Serpukhovsko-Timiryazevskaya and Lyublinsko-Dmitrovskaya lines have eight cars, on the Sokolnicheskaya line seven cars and on the Koltsevaya and Kakhovskaya lines six cars. The Filyovskaya and Arbatsko-Pokrovskaya lines had

History.

The first plans for a metro system in Moscow date back to the Russian Empire but were postponed by World War I, the October Revolution and the Russian Civil War. In 1923, the Moscow City Council formed the Underground Railway Design Office at the Moscow Board of Urban Railways. It carried out preliminary studies, and by 1928 had developed a project for the first route from Sokolniki to the city centre. At the same time, an offer was made to the German company Siemens Bauunion to submit its own project for the same route. In June 1931, the decision to begin construction of the Moscow Metro was made by the Central Committee of the Communist Party of the Soviet Union. In January 1932 the plan for the first lines was approved, and on 21 March 1933 the Soviet government approved a plan for 10 lines with a total route length of.  The first lines were built using the Moscow general plan designed by Lazar Kaganovich, along with his project managers (notably Ivan M. Kuznetsov and, later, Isaac Y. Segal) in the 1930s-1950s, and the Metro was named after him until 1955 "()". The Moscow Metro construction engineers consulted with their counterparts from the London Underground, the world's oldest metro system. Partly because of this connection, the design of the Gants Hill tube station in London, which was completed much later, is reminiscent of a Moscow Metro station.  Soviet workers did the labor and the art work, but the main engineering designs, routes, and construction plans were handled by specialists recruited from the London Underground. The Britons called for tunneling instead of the "cut-and-cover" technique, the use of escalators instead of lifts, the routes and the design of the rolling stock. The paranoia of the NKVD was evident when the secret police arrested numerous British engineers for espionage because they gained an in-depth knowledge of the city's physical layout. Engineers for the Metropolitan-Vickers Electrical Company (Metrovick) were given a show trial and deported in 1933, ending the role of British business in the USSR.

First four stages of construction.

The first line was opened to the public on 15 May 1935 at 07:00 am. It was long and included 13 stations. The day was celebrated as a technological and ideological victory for socialism (and, by extension, Stalinism). An estimated 285,000 people rode the Metro at its debut, and its design was greeted with pride; street celebrations included parades, plays and concerts. The Bolshoi Theatre presented a choral performance by 2,200 Metro workers; 55,000 colored posters (lauding the Metro as the busiest and fastest in the world) and 25,000 copies of

Cold War era.

The beginning of the Cold War led to the construction of a deep section of the Arbatsko-Pokrovskaya Line. The stations on this line were planned as shelters in the event of nuclear war. After finishing the line in 1953 the upper tracks between Ploshchad Revolyutsii and Kiyevskaya were closed, and later reopened in 1958 as a part of the Filyovskaya Line. In the further development of the Metro the term "stages" was not used any more, although sometimes the stations opened in 1957–1959 are referred to as the "fifth stage".  Other stations, too, were supplied with tight gates and life-sustenance systems to function as nuclear shelters.  During the late 1950s the architectural extravagance of new

Stalinist ideals.

Publicizing the metro.

The Moscow Metro was one of the USSR's most ambitious architectural projects. The metro's artists and architects worked to design a structure that embodied "svet" (radiance or brilliance) and "svetloe budushchee" (a radiant future). With their reflective marble walls, high ceilings and grand chandeliers, many Moscow Metro stations have been likened to an "artificial underground sun". This palatial underground environment reminded riders that their tax rubles had been well spent on "svetloe budushchee".  The chief lighting engineer was Abram Damsky, a

Industrialization.

Stalin's first five-year plan (1928–1932) facilitated rapid industrialization to build a socialist motherland. The plan was ambitious, seeking to reorient an agrarian society towards industrialism. It was Stalin's fanatical energy, large-scale planning, and smart resource distribution that kept up the incredible pace of industrialization. The first five-year plan was instrumental in the completion of the Moscow Metro; without industrialization, the Soviet Union would not have had the raw materials necessary for the project. For example, steel was a main component of many subway

Mobilization.

The Communist Party had the power to mobilize; because the party was a single source of control, it could focus its resources and inspire its people. The most notable example of mobilization in the Soviet Union occurred during World War II. The country also mobilized in order to complete the Moscow Metro with unprecedented speed. One of the main motivation factors of the mobilization was to overtake the West and prove that a socialist metro could surpass capitalist designs. It was especially important to the Soviet Union that socialism succeed industrially, technologically, and artistically in the 1930s, since capitalism was at a low ebb during the Great Depression.  The person in charge of Metro mobilization

Patriotic influences.

When the Metro opened in 1935 it immediately became the centrepiece of the transportation system. More than that, it was a Stalinist device to awe and control the populace, and give them an appreciation of Soviet realist art. It became the prototype for future Soviet large-scale technologies. Kaganovich was in charge; he designed the subway so that citizens would absorb the values and ethos of Stalinist civilization as they rode. The artwork of the 13 original stations became nationally and internationally famous. For example, the Sverdlov Square subway station featured porcelain bas-reliefs depicting the daily life of the Soviet peoples, and the bas-reliefs at

Moscow Central Circle urban railway (Line 14).

A proposal to convert the Little Ring of the Moscow Railway into a metropolitan railway with frequent passenger service was announced in 2012. New track was laid and stations were built between 2014

Logo.

The first line of the Moscow Metro was launched in 1935, complete with the first logo, the capital M paired with the text "МЕТРО". There is no accurate information about the author of the logo, so it is often attributed to the architects of the first stations – Samuil Kravets, Ivan Taranov and Nadezhda Bykova. It is noteworthy, however, that

Ticketing.

From the 1960s to the 1990s, the cost of a ride was five kopecks (1/20 of a Soviet ruble). The fare has been steadily rising since 1991, hastened by inflation (taking into account the 1998 revaluation of the ruble by a factor of 1,000). Effective February 2017, one ride costs 55 rubles (approx. 1 US dollar). Discounts (up to 33 percent) are available when buying a multiple-trip ticket (starting with twenty-trip cards), and children under age seven can travel free with their parents.  Tickets are available for a fixed number of trips, regardless of distance traveled or number of transfers. Monthly and yearly passes are also available. Fare enforcement takes place at the points of entry. Once a passenger has entered the Metro system, there are no further ticket checks – one can ride to any number of stations and make transfers within the system freely. Transfers to other public-transport systems (such as bus, tram, trolleybus) are not covered by the ticket. Transfer to monorail is free within 90 minutes.  Before 1991, turnstiles accepted coins; however, with the start of hyperinflation plastic tokens of various design were used. Disposable magnetic stripe cards were introduced in 1993 on a trial basis, and used as unlimited monthly tickets between 1996 and 1998. The sale of tokens ended on 1 January 1999, and they stopped being accepted in February 1999; from that time, magnetic cards were used as tickets with a fixed number of trips.  On 1 September 1998, the Moscow Metro became the first metro system in Europe to fully implement contactless smart cards, known as Transport Cards. The card has an unlimited number of trips and may be programmed for 30, 90 or 365 days. The first purchase includes a one-time cost of 50 rubles, and its active lifetime is projected as 31⁄2 years; defective cards are exchanged at no cost. Unlimited cards are also available for students at reduced price (as of 2017, 365 rubles—or about $US6—for a calendar month of unlimited usage) for a one-time cost of 70 rubles. Transport Cards impose a delay for each consecutive use; i.e. the card can not be used for seven minutes after the user has passed through the turnstile.  In January 2007, Moscow Metro began replacing magnetic cards with contactless disposable tickets based on NXP's MIFARE Ultralight technology. Ultralight tickets are available for a fixed number of trips in 1, 2, 5, 10, 20 and 60-trip denominations (valid for 5 or 90 days from the day of purchase) and as a monthly ticket, only valid for a selected calendar month and limited to 70 trips. The sale of magnetic cards stopped 16 January 2008 and magnetic cards stopped being accepted in late 2008, making the Moscow metro the world's first major public-transport system to run exclusively on a contactless automatic fare-collection system.  In August 2004, the city government launched the Muscovite's Social Card program. Social Cards are free smart cards issued for the elderly and other groups of citizens officially registered as residents of Moscow or the Moscow region; they offer discounts in shops and pharmacies, and double as credit cards issued by the Bank of Moscow. Social Cards can be used for unlimited free access to the city's public-transport system, including the Moscow Metro; while they do not feature the time delay, they include a photograph and are non-transferable.  Since 2006, several banks have issued credit cards which double as Ultralight cards and are accepted at turnstiles. The fare is passed to the bank and the payment is withdrawn from the owner's bank account at the end of the calendar month, using a discount rate based on the number of trips that month (for up to 70 trips, the cost of each trip is prorated from current Ultralight rates; each additional trip costs 24.14 rubles). Partner banks include the Bank of Moscow, CitiBank, Rosbank, Alfa-Bank and Avangard Bank.  On 2 April 2013 Moscow Transport Department introduced a smart card based transport electronic wallet called "Troika". There are also three more smart cards has been launched - "Ediniy" card, a universal card for all city-owned public transport operated by Mosgortrans and Moscow Metro, "90 minutes" card, an unlimited "90-minute" card and "TAT" card for surface public transport operated by Mosgortrans.  In 2013, as a way to promote both the "Olympic Games in Sochi and active lifestyles, Moscow Metro installed a vending machine that gives commuters a free ticket in exchange for doing 30 squats."  From the first quarter of 2015 ticket windows at stations started to accept bank cards for fare payment. Passengers were also able to start using contactless payment systems, such as PayPass technology on MasterCard and Maestro Visa PayWave on Visa cards, at fare gates to enter the system.  Fare gates at stations started in September 2015 to accept payment using mobile ticketing, a system which the Metro calls Mobile Ticket (Мобильный билет). Customers wishing to use this method of payment must exchange their existing SIM card for one that supports Near Field Communication technology. Applicable fares are the same as on the Troika card.  Customers are able to use Mobile Ticket on Moscow's surface transport.  The Moscow Metro originally announced plans to launch the mobile ticketing service with Mobile TeleSystems (MTS) in 2010.

Expansions.

Since the turn of the 21st century several projects have been completed, and more are underway. The first was the Annino-Butovo extension, which extended the Serpukhovsko-Timiryazevskaya Line from Prazhskaya to Ulitsa Akademika Yangelya in 2000, Annino in 2001 and Bulvar Dmitriya Donskogo in 2002. Its continuation, an elevated Butovskaya Line, was inaugurated in 2003. Vorobyovy Gory station, which initially opened in 1959 and was forced to close in 1983 after the concrete used to build the bridge was found to be defective, was rebuilt and reopened after many years in 2002. Another recent project included building a branch off the Filyovskaya Line to the Moscow International Business Center. This included Vystavochnaya (opened in 2005) and Mezhdunarodnaya (opened in 2006).  The Strogino–Mitino extension began with Park Pobedy in 2003. Its first stations (an expanded Kuntsevskaya and Strogino) opened in January 2008, and Slavyansky Bulvar followed in September. Myakinino, Volokolamskaya and Mitino opened in December 2009. Myakinino station was built by a state-private financial partnership, unique in Moscow Metro history. A new terminus, Pyatnitskoye Shosse, was completed in December 2012.  After many years of construction, the long-awaited Lyublinskaya Line extension was inaugurated with Trubnaya in August 2007 and Sretensky Bulvar in December of that year. In June 2010, it was extended northwards with the Dostoyevskaya and Maryina Roscha stations. In December 2011, the Lyublinskaya Line was expanded southwards by three stations and connected to the Zamoskvoretskaya Line, with the Alma-Atinskaya station opening on the latter in December 2012. The Kalininskaya Line was extended past the Moscow Ring Road in August 2012 with Novokosino station.  In 2011 works began on the Third Interchange Contour that is set to take the pressure off the Koltsevaya Line. Eventually the new line will attain a shape of the second ring with connections to all lines (except Koltsevaya and Butovskaya).  In 2013 the Tagansko-Krasnopresnenskaya Line was extended after several delays to the south-eastern districts of Moscow outside the Ring Road with the opening of Zhulebino and Lermontovsky Prospekt stations. Originally scheduled for 2013, a new segment of the Kalininskaya Line between Park Pobedy and Delovoy Tsentr (separate from the main part) was opened in January 2014, while the underground extension of Butovskaya Line northwards to offer a transfer to the Kaluzhsko-Rizhskaya Line was completed in February. Spartak, a station on the Tagansko-Krasnopresnenskaya Line that remained unfinished for forty years, was finally opened in August 2014. The first stage of the southern extension of the Sokolnicheskaya Line, the Troparyovo station, opened in December 2014.

Metro 2.

It has been alleged that a second and deeper metro system code-named "D-6", designed for emergency evacuation of key city personnel in case of nuclear attack during the Cold War, exists under military jurisdiction. It is believed that it consists of a single track connecting the Kremlin, chief HQ (General Staff–"Genshtab"), Lubyanka (FSB Headquarters), the Ministry of Defence and several other secret

Notable incidents.

1977 bombing.

On 8 January 1977, a bomb was reported to have killed 7 and seriously injured 33.

1981 station fires.

In June 1981, seven bodies were seen being removed from the Oktyabrskaya

1982 escalator accident.

A fatal accident occurred on 17 February 1982 due to an escalator collapse at the

2000 bombings.

On 8 August 2000, a strong blast in a Metro underpass at Pushkinskaya metro station in the center

2004 bombings.

On 6 February 2004, an explosion wrecked a train between the Avtozavodskaya and Paveletskaya stations on the Zamoskvoretskaya Line, killing 41 and wounding over 100. Chechen

2005 Moscow blackout.

On 25 May 2005, a citywide blackout halted operation on some lines. The following lines, however, continued operations: Sokolnicheskaya, Zamoskvoretskaya from Avtozavodskaya to Rechnoy Vokzal, Arbatsko-Pokrovskaya, Filyovskaya, Koltsevaya, Kaluzhsko-Rizhskaya from Bitsevskiy Park to Oktyabrskaya-Radialnaya and from Prospekt Mira-Radialnaya to Medvedkovo, Tagansko-Krasnopresnenskaya, Kalininskaya, Serpukhovsko-Timiryazevskaya from Serpukhovskaya to Altufyevo and Lyublinskaya from Chkalovskaya to Dubrovka. There

2006 billboard incident.

On 19 March 2006 a construction pile from an unauthorized billboard installation was driven

2010 bombing.

On 29 March 2010, two bombs exploded on the Sokolnicheskaya Line, killing 40 and injuring 102 others. The first bomb went off at the Lubyanka station on the Sokolnicheskaya Line at 7:56, during the morning rush hour.

2014 pile incident.

On 25 January 2014, at 15:37 a construction pile from a Moscow Central Circle construction site was driven through a tunnel roof between Avtozavodskaya and Kolomenskaya

2014 derailment.

On 15 July 2014, a train derailed between Park Pobedy

In popular culture.

The Moscow Metro is the central location and namesake for the "Metro" series, where during a nuclear war, Moscow's inhabitants are driven down into the Moscow Metro, which has been designed as a fallout shelter, with the various stations being turned into makeshift settlements.  In 2012, an art film was released about a catastrophe in the Moscow underground.

The Moscow Metro () is a rapid transit system serving Moscow, Russia, and the neighbouring Moscow Oblast cities of Krasnogorsk, Reutov, Lyubertsy and Kotelniki. Opened in 1935 with one line and 13 stations, it was the first underground railway system in the Soviet Union., the Moscow Metro, excluding the Moscow Central Circle and Moscow Monorail, has 232 stations (263 with Moscow Central Circle) and its route length is, making it the fourth longest in the world and longest outside China. The system is mostly underground, with the deepest section underground at the Park Pobedy station, one of the world's deepest underground stations. It is the busiest metro system in Europe, and is considered a tourist attraction in itself.

莫斯科地铁(),全称为列宁莫斯科市地铁系统(),是世界上使用率第六高的地下轨道系统。其中不少车站在建设的时候融入了卓越的设计风格以及大理石立柱的设计,使得莫斯科地铁的富丽堂皇的程度在世界上是首屈一指的,也影响了很多前苏联地区及社会主义国家的地铁设计。


History.

Background.

There were long discussions before signing the union treaty. Lithuanian magnates were afraid of losing much of their powers, since the union would make their legal status equal to that of the much more numerous Polish lower nobility. Lithuania had been increasingly on the losing side of the Muscovite-Lithuanian Wars, however, and by the second half of the 16th century, it faced the threat of total defeat in the Livonian war and incorporation into Russia. The Polish nobility (the szlachta), on the other hand, were reluctant to offer help to Lithuania without receiving anything in exchange. Nevertheless, the Polish and Lithuanian elites strengthened personal bonds and had opportunities to plan their united futures during increased military cooperation in the 1560s. Sigismund II Augustus, King of Poland and Grand Duke of Lithuania, seeing the threat to Lithuania and eventually to Poland, pressed for the union, gradually gaining more followers until he felt enough support to evict landowners forcibly who opposed the transition of territory from Lithuania to Poland. A clear motivation for Sigismund was that he was the last Jagiello and had no children or brothers who could inherit the throne. Therefore, the Union was an attempt to preserve the continuity of his dynasty's work since the personal (but not constitutional) union of Poland and Lithuania at the marriage of Jadwiga of Poland and Wladyslaw II Jagiello. The Union was one of the constitutional changes required to establish a formal elected monarchy, which would simultaneously reign over both domains.

Sejm of 1569.

The Sejm met in January 1569, near the Polish town of Lublin, but did not reach an agreement. One of the points of contention was the right of Poles to settle and own land in the Grand Duchy. After most of the Lithuanian delegation under the leadership of Vilnius Voivodeship's Mikołaj "Rudy" Radziwiłł left Lublin on 1 March, the king announced the incorporation into the Crown of Podlachia, Volhynia and the Kiev palatinate (on 6 June), with wide approval from the local gentry. Bratslav and eastern Podolia were also transferred to Poland. Those historic lands of Rus' are over half of modern Ukraine and were then a substantial portion of the Grand Duchy of Lithuania's territory. The Rus' nobles there were eager to capitalise on the economic and political opportunities offered by the Polish sphere, and by and large, they wanted their lands to become a part of the Polish Crown.  The Lithuanians were forced to return to the Sejm under the leadership of Jan Hieronimowicz Chodkiewicz (father of Jan Karol Chodkiewicz) and to continue negotiations, using slightly different tactics from those of Radziwiłł. Though the Polish szlachta wanted full incorporation of the Grand Duchy of Lithuania into the Crown, the Lithuanians continued to oppose that and agreed only to a federal state. On 28 June 1569, the last objections were overcome, and on 4 July, an act was accordingly signed by the king at Lublin Castle.

Attempts at modernisation.

The Union of Lublin was superseded by the Constitution of 3 May 1791, under which the federal Commonwealth was to be transformed into a unitary state by King Stanisław August Poniatowski. The status of semi-federal state was restored by the Reciprocal Guarantee of Two Nations. The constitution was not fully implemented, however, and the Commonwealth was ended with the Partitions of Poland in 1795.

Aftermath.

Cultural.

After the Union, the Lithuanian nobles had the same formal rights as the Polish to rule the lands and subjects under their control. However, political advancement in the Catholic-dominated Commonwealth was a different matter.  By the late 15th century, the Polish language was already making rapid inroads among the Lithuanian and Rus' elites. The Lublin Union accelerated the process of Polonization. In culture and social life, both the Polish language and Catholicism became dominant for the Ruthenian nobility, most of whom were initially Ruthenian-speaking and Eastern Orthodox by religion. However the commoners, especially the peasants, continued to speak their own languages and after the Union of Brest converted to Eastern Catholicism.  This eventually created a significant rift between the lower social classes and the nobility in the Lithuanian and Ruthenian areas of the Commonwealth. Some Ruthenian magnates resisted Polonization (like the Ostrogskis) by adhering to Orthodox Christianity, giving generously to the Ruthenian Orthodox Churches and to the Ruthenian schools. However, the pressure of Polonization was harder to resist with each subsequent generation and eventually almost all of the Ruthenian nobility was Polonized.  The Cossack uprisings and foreign interventions led to the partitions of the Commonwealth by Russia, Prussia and Austria in 1772, 1793, and 1795. The Union of Lublin was also temporarily inactive while the Union of Kėdainiai was in effect.  Many historians like Krzysztof Rak consider the Union of Lublin to have created a state similar to the present-day European Union, thus considering the Union (along with the Kalmar Union, the several Acts of Union in the British Isles and other similar treaties) to be a predecessor of the Maastricht Treaty. The former, however, created a state of countries more deeply linked than the present-day European Union.

Economic.

The union brought about the Polish colonization of Ruthenian lands and increasing enserfment of Ruthenian peasantry by the szlachta. Although the conditions for peasants in the Commonwealth was quite dire, compared to the West (see second serfdom), the peasants in the Commonwealth had more freedom than those in Russia; hence peasants (as well as to a lesser extent nobility and merchants) escaping from Russia to the Commonwealth became a major concern for the Russian government, and was one of the factors ultimately leading to the partitions of Poland.  A common coin, the złoty, was introduced.  Execution of crown lands was not extended to the Grand Duchy.

Geographical.

The Union created one of the largest and most populous states in 17th-century Europe (excluding the states not completely in Europe, i.e. the Russian and Ottoman Empires).  Within the Union, Lithuania accepted the loss of Podlaskie, Volhynia, Podolia and the Kiev regions, former territories of the Grand Duchy that were transferred to the Crown of the Kingdom of Poland.

Legal.

The Statutes of Lithuania declared the laws of the Union that conflicted with them to be unconstitutional. The First Statute of Lithuania was also used in the territories of Lithuania that were annexed by Poland shortly before the Union of Lublin (except for Podlaskie). These conflicts between statutory schemes in Lithuania and Poland persisted for many years, and the Third Statute of Lithuania remained in force in territories of the Grand Duchy of Lithuania even after partitions, until 1840.  Attempts to limit the power of Lithuanian magnates (especially the Sapieha family) and unify the laws of the Commonwealth led to the koekwacja praw movement, culminating in the koekwacja reforms of the Election Sejm of 1697 (May–June), confirmed in the General Sejm of 1698 (April) in the document "Porządek sądzenia spraw w Trybunale Wielkiego Księstwa Litewskego".

Military.

Poland provided military aid in the wars after the union of the two entities, which was crucial for the survival of the Grand Duchy. Poland and the Grand Duchy were to have separate military but common defense policies.

Political.

The Union of Lublin provided for merger of the two states, though each retained substantial autonomy, with their own army, treasury, laws and administration. Though the countries were in theory equal, the larger Poland became the dominant partner. Due to population differences, Polish deputies outnumbered Lithuanians in the Sejm by 3:1.  There was to be a single ruler for both Poland and the Grand Duchy, freely elected by the nobility of both nations, and crowned as King of Poland and Grand Duke of Lithuania in Wawel Cathedral, Kraków.  A common parliament, the Sejm, held its sessions in Warsaw; it had 114 deputies from the Polish lands and 48 from Lithuania. The Senate had 113 Polish and 27 Lithuanian senators.  Poland and the Grand Duchy were to have a common foreign policy.

Legacy.

The Union of Lublin was Sigismund's greatest achievement and his greatest failure. Although it created one of the largest states in contemporary Europe, one that endured for over 200 years, Sigismund failed to push through the reforms that would have established a workable political system. He hoped to strengthen the monarchy with the support of the lesser nobility, and to balance the power of lesser nobility and magnates. However, while all the nobility in the Commonwealth was in theory equal under the law, the political power of the magnates was not weakened significantly, and in the end they could too often bribe or coerce their lesser brethren. In addition, the royal power continued to wane, and while the neighbouring states continued to evolve into strong, centralized absolute monarchies, the Commonwealth slid with its Golden Liberty into a political anarchy that eventually cost it its very existence.  Today's Republic of Poland considers itself a successor to the Commonwealth, whereas the pre-World War II Republic of Lithuania saw the creation of the Polish–Lithuanian Commonwealth mostly in a negative light.  The original act document was included in the UNESCO Memory of the World Register in 2017.

The Union of Lublin (; ) was signed on 1 July 1569, in Lublin, Poland, and created a single state, the Polish–Lithuanian Commonwealth, one of the largest countries in Europe at the time. It replaced the personal union of the Crown of the Kingdom of Poland and the Grand Duchy of Lithuania with a real union and an elective monarchy, since Sigismund II Augustus, the last of the Jagiellons, remained childless after three marriages. In addition, the autonomy of Royal Prussia was largely abandoned. The Duchy of Livonia, tied to Lithuania in real union since the Union of Grodno (1566), became a Polish–Lithuanian condominium.

卢布林联合(;)是在1569年7月1日成立的一个共主邦联。随着卢布林联合的成立,波兰立陶宛联邦诞生。立陶宛大公国、王室普鲁士与波兰王国两国合并。两国结盟后被正式称为联邦(Rzeczpospolita)。波兰-立陶宛由原来的君合国(共主邦联)转变为选王制的政合国。


Scope.

Difference between equilibrium and non-equilibrium thermodynamics.

A profound difference separates equilibrium from non-equilibrium thermodynamics. Equilibrium thermodynamics ignores the time-courses of physical processes. In contrast, non-equilibrium thermodynamics attempts to describe their time-courses in continuous detail.  Equilibrium thermodynamics restricts its considerations to processes that have initial and final states of thermodynamic equilibrium; the time-courses of processes are deliberately ignored. Consequently, equilibrium thermodynamics allows processes that pass through states far from thermodynamic equilibrium, that cannot be described even by the variables admitted for non-equilibrium thermodynamics, such as time rates of change of temperature and pressure. For example, in equilibrium thermodynamics, a process is allowed to include even a violent explosion that cannot be described by non-equilibrium thermodynamics. Equilibrium thermodynamics does, however, for theoretical development, use the idealized concept of the "quasi-static process". A quasi-static process is a conceptual (timeless and physically impossible) smooth mathematical passage along a continuous path of states of thermodynamic equilibrium. It is an exercise in differential geometry rather than a process that could occur in actuality.  Non-equilibrium thermodynamics, on the other hand, attempting to describe continuous time-courses, needs its state variables to have a very close connection with those of equilibrium thermodynamics. This profoundly restricts the scope of non-equilibrium thermodynamics, and places heavy demands on its conceptual framework.

Non-equilibrium state variables.

The suitable relationship that defines non-equilibrium thermodynamic state variables is as follows. On occasions when the system happens to be in states that are sufficiently close to thermodynamic equilibrium, non-equilibrium state variables are such that they can be measured locally with sufficient accuracy by the same techniques as are used to measure thermodynamic state variables, or by corresponding time and space derivatives, including fluxes of matter and energy. In general, non-equilibrium thermodynamic systems are spatially and temporally non-uniform, but their non-uniformity still has a sufficient degree of smoothness to support the existence of suitable time and space derivatives of non-equilibrium state variables. Because of the spatial non-uniformity, non-equilibrium state variables that correspond to extensive thermodynamic state variables have to be defined as spatial densities of the corresponding extensive equilibrium state variables. On occasions when the system is sufficiently close to thermodynamic equilibrium, intensive non-equilibrium state variables, for example temperature and pressure, correspond closely with equilibrium state variables. It is necessary that measuring probes be small enough, and rapidly enough responding, to capture relevant non-uniformity. Further, the non-equilibrium state variables are required to be mathematically functionally related to one another in ways that suitably resemble corresponding relations between equilibrium thermodynamic state variables. In reality, these requirements are very demanding, and it may be difficult or practically, or even theoretically, impossible to satisfy them. This is part of why non-equilibrium thermodynamics is a work in progress.

Overview.

Non-equilibrium thermodynamics is a work in progress, not an established edifice. This article is an attempt to sketch some approaches to it and some concepts important for it.  Some concepts of particular importance for non-equilibrium thermodynamics include time rate of dissipation of energy (Rayleigh 1873, Onsager 1931, also), time rate of entropy production (Onsager 1931), thermodynamic fields, dissipative structure, and non-linear dynamical structure.  One problem of interest is the thermodynamic study of non-equilibrium steady states, in which entropy production and some flows are non-zero, but there is no time variation of physical variables.  One initial approach to non-equilibrium thermodynamics is sometimes called 'classical irreversible thermodynamics'. There are other approaches to non-equilibrium thermodynamics, for example extended irreversible thermodynamics, and generalized thermodynamics, but they are hardly touched on in the present article.

Quasi-radiationless non-equilibrium thermodynamics of matter in laboratory conditions.

According to Wildt (see also Essex), current versions of non-equilibrium thermodynamics ignore radiant heat; they can do so because they refer to laboratory quantities of matter under laboratory conditions with temperatures well below those of stars. At laboratory temperatures, in laboratory quantities of matter, thermal radiation is weak and can be practically nearly ignored. But, for example, atmospheric physics is concerned with large amounts of matter, occupying cubic kilometers, that, taken as a whole, are not within the range of laboratory quantities; then thermal radiation cannot be ignored.

Local equilibrium thermodynamics.

The terms 'classical irreversible thermodynamics' and 'local equilibrium thermodynamics' are sometimes used to refer to a version of non-equilibrium thermodynamics that demands certain simplifying assumptions, as follows. The assumptions have the effect of making each very small volume element of the system effectively homogeneous, or well-mixed, or without an effective spatial structure, and without kinetic energy of bulk flow or of diffusive flux. Even within the thought-frame of classical irreversible thermodynamics, care is needed in choosing the independent variables for systems. In some writings, it is assumed that the intensive variables of equilibrium thermodynamics are sufficient as the independent variables for the task (such variables are considered to have no'memory', and do not show hysteresis); in particular, local flow intensive variables are not admitted as independent variables; local flows are considered as dependent on quasi-static local intensive variables.  Also it is assumed that the local entropy density is the same function of the other local intensive variables as in equilibrium; this is called the local thermodynamic equilibrium assumption (see also Keizer (1987)). Radiation is ignored because it is transfer of energy between regions, which can be remote from one another. In the classical irreversible thermodynamic approach, there is allowed very small spatial variation, from very small volume element to adjacent very small volume element, but it is assumed that the global entropy of the system can be found by simple spatial integration of the local entropy density; this means that spatial structure cannot contribute as it properly should to the global entropy assessment for the system. This approach assumes spatial and temporal continuity and even differentiability of locally defined intensive variables such as temperature and internal energy density. All of these are very stringent demands. Consequently, this approach can deal with only a very limited range of phenomena. This approach is nevertheless valuable because it can deal well with some macroscopically observable phenomena.  In other writings, local flow variables are considered; these might be considered as classical by analogy with the time-invariant long-term time-averages of flows produced by endlessly repeated cyclic processes; examples with flows are in the thermoelectric phenomena known as the Seebeck and the Peltier effects, considered by Kelvin in the nineteenth century and by Lars Onsager in the twentieth. These effects occur at metal junctions, which were originally effectively treated as two-dimensional surfaces, with no spatial volume, and no spatial variation.

Local equilibrium thermodynamics with materials with "memory".

A further extension of local equilibrium thermodynamics is to allow that materials may have "memory", so that their constitutive equations depend not only on present values but also on past values of local equilibrium variables. Thus time comes into the picture more deeply than for time-dependent local equilibrium thermodynamics with memoryless materials, but fluxes are not independent variables of state.

Extended irreversible thermodynamics.

Extended irreversible thermodynamics is a branch of non-equilibrium thermodynamics that goes outside the restriction to the local equilibrium hypothesis. The space of state variables is enlarged by including the fluxes of mass, momentum and energy and eventually higher order fluxes. The formalism is well-suited for describing high-frequency processes and small-length scales materials.

Basic concepts.

There are many examples of stationary non-equilibrium systems, some very simple, like a system confined between two thermostats at different temperatures or the ordinary Couette flow, a fluid enclosed between two flat walls moving in opposite directions and defining non-equilibrium conditions at the walls. Laser action is also a non-equilibrium process, but it depends on departure from local thermodynamic equilibrium and is thus beyond the scope of classical irreversible thermodynamics; here a strong temperature difference is maintained between two molecular degrees of freedom (with molecular laser, vibrational and rotational molecular motion), the requirement for two component 'temperatures' in the one small region of space, precluding local thermodynamic equilibrium, which demands that only one temperature be needed. Damping of acoustic perturbations or shock waves are non-stationary non-equilibrium processes. Driven complex fluids, turbulent systems and glasses are other examples of non-equilibrium systems.  The mechanics of macroscopic systems depends on a number of extensive quantities. It should be stressed that all systems are permanently interacting with their surroundings, thereby causing unavoidable fluctuations of extensive quantities. Equilibrium conditions of thermodynamic systems are related to the maximum property of the entropy. If the only extensive quantity that is allowed to fluctuate is the internal energy, all the other ones being kept strictly constant, the temperature of the system is measurable and meaningful. The system's properties are then most conveniently described using the thermodynamic potential Helmholtz free energy ("A" = "U" - "TS"), a Legendre transformation of the energy. If, next to fluctuations of the energy, the macroscopic dimensions (volume) of the system are left fluctuating, we use the Gibbs free energy ("G" = "U" + "PV" - "TS"), where the system's properties are determined both by the temperature and by the pressure.  Non-equilibrium systems are much more complex and they may undergo fluctuations of more extensive quantities. The boundary conditions impose on them particular intensive variables, like temperature gradients or distorted collective motions (shear motions, vortices, etc.), often called thermodynamic forces. If free energies are very useful in equilibrium thermodynamics, it must be stressed that there is no general law defining stationary non-equilibrium properties of the energy as is the second law of thermodynamics for the entropy in equilibrium thermodynamics. That is why in such cases a more generalized Legendre transformation should be considered. This is the extended Massieu potential. By definition, the entropy ("S") is a function of the collection of extensive quantities formula_1. Each extensive quantity has a conjugate intensive variable formula_2 (a restricted definition of intensive variable is used here by comparison to the definition given in this link) so that:  We then define the extended Massieu function as follows:  where formula_5 is Boltzmann's constant, whence  The independent variables are the intensities.  Intensities are global values, valid for the system as a whole. When boundaries impose to the system different local conditions, (e.g. temperature differences), there are intensive variables representing the average value and others representing gradients or higher moments. The latter are the thermodynamic forces driving fluxes of extensive properties through the system.  It may be shown that the Legendre transformation changes the maximum condition of the entropy (valid at equilibrium) in a minimum condition of the extended Massieu function for stationary states, no matter whether at equilibrium or not.

Stationary states, fluctuations, and stability.

In thermodynamics one is often interested in a stationary state of a process, allowing that the stationary state include the occurrence of unpredictable and experimentally unreproducible fluctuations in the state of the system. The fluctuations are due to the system's internal sub-processes and to exchange of matter or energy with the system's surroundings that create the constraints that define the process.  If the stationary state of the process is stable, then the unreproducible fluctuations involve local transient decreases of entropy. The reproducible response of the system is then to increase the entropy back to its maximum by irreversible processes: the fluctuation cannot be reproduced with a significant level of probability. Fluctuations about stable stationary states are extremely small except near critical points (Kondepudi and Prigogine 1998, page 323). The stable stationary state has a local maximum of entropy and is locally the most reproducible state of the system. There are theorems about the irreversible dissipation of fluctuations. Here 'local' means local with respect to the abstract space of thermodynamic coordinates of state of the system.  If the stationary state is unstable, then any fluctuation will almost surely trigger the virtually explosive departure of the system from the unstable stationary state. This can be accompanied by increased export of entropy.

Local thermodynamic equilibrium.

The scope of present-day non-equilibrium thermodynamics does not cover all physical processes. A condition for the validity of many studies in non-equilibrium thermodynamics of matter is that they deal with what is known as "local thermodynamic equilibrium".

Ponderable matter.

"Local thermodynamic equilibrium of matter" (see also Keizer (1987) means that conceptually, for study and analysis, the system can be spatially and temporally divided into 'cells' or'micro-phases' of small (infinitesimal) size, in which classical thermodynamical equilibrium conditions for matter are fulfilled to good approximation. These conditions are unfulfilled, for example, in very rarefied gases, in which molecular collisions are infrequent; and in the boundary layers of a star, where radiation is passing energy to space; and for interacting fermions at very low temperature, where dissipative processes become ineffective. When these 'cells' are defined, one admits that matter and energy may pass freely between contiguous 'cells', slowly enough to leave the 'cells' in their respective individual local thermodynamic equilibria with respect to intensive variables.  One can think here of two'relaxation times' separated by order of magnitude.<ref name="Zubarev 1971/1974">Zubarev D. N.,(1974). "Nonequilibrium Statistical Thermodynamics", translated from the Russian by P.J. Shepherd, New York, Consultants Bureau. ;.</ref> The longer relaxation time is of the order of magnitude of times taken for the macroscopic dynamical structure of the system to change. The shorter is of the order of magnitude of times taken for a single 'cell' to reach local thermodynamic equilibrium. If these two relaxation times are not well separated, then the classical non-equilibrium thermodynamical concept of local thermodynamic equilibrium loses its meaning and other approaches have to be proposed, see for instance Extended irreversible thermodynamics. For example, in the atmosphere, the speed of sound is much greater than the wind speed; this favours the idea of local thermodynamic equilibrium of matter for atmospheric heat transfer studies at altitudes below about 60 km where sound propagates, but not above 100 km, where, because of the paucity of intermolecular collisions, sound does not propagate.

Milne's definition in terms of radiative equilibrium.

Edward A. Milne, thinking about stars, gave a definition of 'local thermodynamic equilibrium' in terms of the thermal radiation of the matter in each small local 'cell'. He defined 'local thermodynamic equilibrium' in a 'cell' by requiring that it macroscopically absorb and spontaneously emit radiation as if it were in radiative equilibrium in a cavity at the temperature of the matter of the 'cell'. Then it strictly obeys Kirchhoff's law of equality of radiative emissivity and absorptivity, with a black body source function. The key to local thermodynamic equilibrium here is that the rate of collisions of ponderable matter particles such as molecules should far exceed the rates of creation and annihilation of photons.

Entropy in evolving systems.

It is pointed out by W.T. Grandy Jr, that entropy, though it may be defined for a non-equilibrium system is—when strictly considered—only a macroscopic quantity that refers to the whole system, and is not a dynamical variable and in general does not act as a local potential that describes local physical forces. Under special circumstances, however, one can metaphorically think as if the thermal variables behaved like local physical forces. The approximation that constitutes classical irreversible thermodynamics is built on this metaphoric thinking.  This point of view shares many points in common with the concept and the use of entropy in continuum thermomechanics, which evolved completely independently of statistical mechanics and maximum-entropy principles.

Entropy in non-equilibrium.

To describe deviation of the thermodynamic system from equilibrium, in addition to constitutive variables formula_7 that are used to fix the equilibrium state, as was described above, a set of variables formula_8 that are called "internal variables" have been introduced. The equilibrium state is considered to be stable and the main property of the internal variables, as measures of non-equilibrium of the system, is their trending to disappear; the local law of disappearing can be written as relaxation equation for each internal variable  where formula_9 is a relaxation time of a corresponding variables. It is convenient to consider the initial value formula_10 are equal to zero. The above equation is valid for small deviations from equilibrium; The dynamics of internal variables in general case is considered by Pokrovskii.  Entropy of the system in non-equilibrium is a function of the total set of variables  The essential contribution to the thermodynamics of the non-equilibrium systems was brought by Prigogine, when he and his collaborators investigated the systems of chemically reacting substances. The stationary states of such systems exists due to exchange both particles and energy with the environment. In section 8 of the third chapter of his book, Prigogine has specified three contributions to the variation of entropy of the considered system at the given volume and constant temperature formula_11. The increment of entropy formula_12 can be calculated according to the formula  The first term on the right hand side of the equation presents a stream of thermal energy into the system; the last term -- a stream of energy into the system coming with the stream of particles of substances formula_13 that can be positive or negative, formula_14 is chemical potential of substance formula_15. The middle term in (1) depicts energy dissipation (entropy production) due to the relaxation of internal variables formula_16. In the case of chemically reacting substances, which was investigated by Prigogine, the internal variables appear to be measures of incompleteness of chemical reactions, that is measures of how much the considered system with chemical reactions is out of equilibrium. The theory can be generalised, to consider any deviation from the equilibrium state as an internal variable, so that we consider the set of internal variables formula_16 in equation (1) to consist of the quantities defining not only degrees of completeness of all chemical reactions occurring in the system, but also the structure of the system, gradients of temperature, difference of concentrations of substances and so on.

Flows and forces.

The fundamental relation of classical equilibrium thermodynamics  expresses the change in entropy formula_19 of a system as a function of the intensive quantities temperature formula_20, pressure formula_21 and formula_22 chemical potential formula_23 and of the differentials of the extensive quantities energy formula_24, volume formula_25 and formula_22 particle number formula_27.  Following Onsager (1931,I), let us extend our considerations to thermodynamically non-equilibrium systems. As a basis, we need locally defined versions of the extensive macroscopic quantities formula_24, formula_25 and formula_27 and of the intensive macroscopic quantities formula_20, formula_21 and formula_23.  For classical non-equilibrium studies, we will consider some new locally defined intensive macroscopic variables. We can, under suitable conditions, derive these new variables by locally defining the gradients and flux densities of the basic locally defined macroscopic quantities.  Such locally defined gradients of intensive macroscopic variables are called 'thermodynamic forces'. They 'drive' flux densities, perhaps misleadingly often called 'fluxes', which are dual to the forces. These quantities are defined in the article on Onsager reciprocal relations. Establishing the relation between such forces and flux densities is a problem in statistical mechanics. Flux densities (formula_34) may be coupled. The article on Onsager reciprocal relations considers the stable near-steady thermodynamically non-equilibrium regime, which has dynamics linear in the forces and flux densities.  In stationary conditions, such forces and associated flux densities are by definition time invariant, as also are the system's locally defined entropy and rate of entropy production. Notably, according to Ilya Prigogine and others, when an open system is in conditions that allow it to reach a stable stationary thermodynamically non-equilibrium state, it organizes itself so as to minimize total entropy production defined locally. This is considered further below.  One wants to take the analysis to the further stage of describing the behaviour of surface and volume integrals of non-stationary local quantities; these integrals are macroscopic fluxes and production rates. In general the dynamics of these integrals are not adequately described by linear equations, though in special cases they can be so described.

Onsager reciprocal relations.

Following Section III of Rayleigh (1873), Onsager (1931, I) showed that in the regime where both the flows (formula_34) are small and the thermodynamic forces (formula_36) vary slowly, the rate of creation of entropy formula_37 is linearly related to the flows:  and the flows are related to the gradient of the forces, parametrized by a matrix of coefficients conventionally denoted formula_39:  from which it follows that:  The second law of thermodynamics requires that the matrix formula_39 be positive definite. Statistical mechanics considerations involving microscopic reversibility of dynamics imply that the matrix formula_39 is symmetric. This fact is called the "Onsager reciprocal relations".  The generalization of the above equations for the rate of creation of entropy was given by Pokrovskii.

Speculated extremal principles for non-equilibrium processes.

Until recently, prospects for useful extremal principles in this area have seemed clouded. Nicolis (1999) concludes that one model of atmospheric dynamics has an attractor which is not a regime of maximum or minimum dissipation; she says this seems to rule out the existence of a global organizing principle, and comments that this is to some extent disappointing; she also points to the difficulty of finding a thermodynamically consistent form of entropy production. Another top expert offers an extensive discussion of the possibilities for principles of extrema of entropy production and of dissipation of energy: Chapter 12 of Grandy (2008) is very cautious, and finds difficulty in defining the 'rate of internal entropy production' in many cases, and finds that sometimes for the prediction of the course of a process, an extremum of the quantity called the rate of dissipation of energy may be more useful than that of the rate of entropy production; this quantity appeared in Onsager's 1931 origination of this subject. Other writers have also felt that prospects for general global extremal principles are clouded. Such writers include Glansdorff and Prigogine (1971), Lebon, Jou and Casas-Vásquez (2008), and Šilhavý (1997).  A recent proposal may perhaps bypass those clouded prospects.

Applications.

Non-equilibrium thermodynamics has been successfully applied to describe biological processes such as protein folding/unfolding and transport through membranes. It is also used to give a description of the dynamics of nanoparticles, which can be out of equilibrium in systems where catalysis and electrochemical conversion is involved. Also, ideas from non-equilibrium thermodynamics and the informatic theory of entropy have been adapted to describe general economic systems.

Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of variables (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. It relies on what may be thought of as more or less nearness to thermodynamic equilibrium. Non-equilibrium thermodynamics is a work in progress, not an established edifice.

非平衡态热力学是热力学的一门分支,研究时变热力学系统、不可逆转变和开始系统。非平衡态热力学,和平衡态热力学相对,是研究在非零合力、流动及产生熵,但没有时间变动的隐定态中最成功的一门学科。早期所发现的非平衡态系统为BZ化学振荡器。