Competing Styles of Statistical Mechanics: II. Comparison of Theory and Experiment and Further Illustrations
In the present follow-up article of a previous one [1] we illustrate the use of the Unconventional Statistical Mechanics described and discussed in the latter. This is done via the analysis, resorting to Renyi approach, of experimental results in the case of so-called "anomalous" luminescence in nanometric quantum wells in semiconductor heterostructures, and the so-called "anomalous" cyclic voltammetry in fractal-like electrodes in microbatteries. Also a purely theoretical analysis is done in the cases of an ideal gas and of radiation comparing the conventional and unconventional approaches. In all of these situations it is discussed which is the failure to satisfy the Criteria of Efficiency and/or Sufficiency thus requiring to resort to the unconventional approach, and what determines the value of the infoentropic index in each case, and its dependence on the system characteristics. Moreover, on the basis of the results we obtain, it is conjectured that the infoentropic index may satisfy what we call a law defining a "path to sufficiency". PACS: 05.70.Ln; 82.20.Mj; 82.20.Db Keywords: Renyi Statistics; Escort Probability; Fractal Structured Systems; Power Law Properties.
On nonextensive thermo-statistics: systematization, clarification of scope and interpretation, and illustrations
When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard approach to the well established, physically and logically sound, Boltzmann-Gibbs statistics. To circumvent such difficulties, in order to make predictions on properties of the system and looking for an understanding of the physics involved (for example in analyzing the technological characteristics of fractal-structured devices) can be introduced large families of auxiliary statistics. We present here a systematization of these different styles in what can be termed as Unconventional Statistical Mechanics, accompanied of an analysis of the construction and a clarification of its scope and interpretation. As illustrations are derived heterotypical Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann distributions, and several applications including studies of experimental works are briefly described.
Use of laser scanning confocal microscopy for morphological taxonomy and the potential for digital type specimens (e-types)
The use of laser scanning confocal microscopy (LSCM) for creating taxonomic descriptions of copepods is investigated. A new technique is described, which employs a contour filter to process digital LSCM images, allowing taxonomic information to be quickly and accu- rately distilled into a simple illustration. LSCM allows the imaging of whole specimens, which can be rotated and viewed from any angle—a major benefit over light microscopy. Using this tech- nique, it is suggested that taxonomic descriptions can be rapidly produced in a fraction of the time required to produce similar descriptions using traditional light microscopy and hand drawing techniques. Good staining of specimens is, however, essential to produce accurate descriptions and more research is required in this area. The use of LSCM for morphological taxonomy shows great potential, not only for producing taxonomic descriptions, but also providing a comple - mentary adjunct to traditional type specimens in the form of 3D digital 'e-types' deposited in recognised international databases.