Recent Advances in Non-Equilibrium Statistical Mechanics and Its Application

Dear Colleagues,

It is well-known that many natural systems today still remain beyond the scope of currently-known macroscopic thermodynamic methods. Biophysics or physics of the life sciences, for example, will have to deal with fundamental problems in non-equilibrium statistical mechanics. One also finds concepts and models of non-equilibrium physics, in computer science, social science, economy, or in the field of complex systems. However, also well within “classical” physics, major problems remain. A good example is turbulence, the great-unsolved problem of classical physics. Therefore, non-equilibrium statistical mechanics, even today, does not yet exist as a complete and systematic theory, at least, certainly not at the same level as its equilibrium counterpart. However, in recent years, research on non-equilibrium statistical mechanics has made significant progress, in particular in the field of thermodynamics of irreversible processes, viewed as a thermodynamical field theory, of the entropy information theory or the stochastic theory.

The aim of this Special Issue is to encourage scientists to present original and recent developments on non-equilibrium statistical mechanics (stochastic theory, kinetic theory, entropy information theory, etc.) applied to dynamical systems.

One of the objectives of the issue is, therefore, to promote a cross-fertilization among scientists working in a wide range of disciplines ranging from bio-medical dynamical systems to plasmas.

Dynamical and chaotic systems should be treated by Non-equilibrium Statistical Mechanics, e.g., by Stochastic Modeling (Fokker-Planck and/or Master equations, etc.), Kinetic Theory (Boltzmann-equation, Vlasov-Equation, etc.), Entropy Information Theory (Shannon, Rényi, Tsallis entropies, etc.), and Thermodynamics of Irreversible Processes (entropy production, thermodynamically field theories, etc.).

Applications can include mathematical models applied to biomedical systems and plasmas. Concerning plasmas, kinetic theory/non-equilibrium statistical mechanics of weakly turbulent plasmas may be proposed, should be focused on

(i) understanding resonant and non-resonant transport processes of the beam-plasma system, characterizing transitions for increasing beam and/or fluctuation strength.

(ii) understanding the role of sources and collisions in a dissipative system with multiple kinetic resonances.

(iii) complex behaviors, turbulence and self-organization: investigating self-organization of nonlinear systems under the effect of coherent nonlinear interactions vs random perturbations.

Prof. Dr. Giorgio Sonnino
Guest Editor

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