Direct path from microscopic mechanics to Debye shielding, Landau damping and wave-particle interaction
The derivation of Debye shielding and Landau damping from the N-body description of plasmas is performed directly by using Newton’s second law for the N-body system. This is done in a few steps with elementary calculations using standard tools of calculus and no probabilistic setting. Unexpectedly, Debye shielding is encountered together with Landau damping. This approach is shown to be justified in the one-dimensional case when the number of particles in a Debye sphere becomes large. The theory is extended to accommodate a correct description of trapping and chaos due to Langmuir waves. On top of their well-known production of collisional transport, the repulsive deflections of electrons are shown to produce shielding, in such a way that each particle is shielded by all other ones, while keeping in uninterrupted motion.
Complexity and simplicity of plasmas
This paper has two main parts. The first one presents a direct path from microscopic dynamics to Debye screening, Landau damping and collisional transport. It shows there is more simplicity in microscopic plasma physics than previously thought. The second part is more subjective. It describes some difficulties in facing plasma complexity in general, suggests an inquiry about the methods used empirically to tackle complex systems, discusses the teaching of plasma physics as a physics of complexity, and proposes new directions to face the inflation of information.
Entropy Methods for the Boltzmann Equation
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level. 
 
During a special semester on Hydrodynamic Limits at the Centre Emile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.