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Statistical Mechanics

A section of Entropy (ISSN 1099-4300).

Section Information

Statistical mechanics is a branch of physics that aims to relate the microscopic with the macroscopic properties of matter by using concepts developed in the field of probability theory and thermodynamics. It is a successful combination of statistics and mechanics arising from the union of the basic laws of classical or quantum mechanics with the laws of the large numbers.

The foundations of statistical mechanics lie in the thermodynamics theory developed at the end of the nineteenth century. The first to analyse transport phenomena with statistical methods was Clausius, by introducing the concept of the mean free path. He also introduced the famous “Stosszahlansatz” hypothesis that played a prominent role in the succeeding works of Boltzmann. In the pioneering paper on the “Zusammeuhang zwischen den Satzen iiber das Verhalten mehratomiger Gasmolekiile mit Jacobi's Princip des letzten Multiplicators”, Boltzmann considers explicitly a great number of systems, their distribution in phase space and the permanence of this distribution in time. Another impressive contribution to the theory is represented by Maxwell’s work on the kinetic theory of gases derived from what is now called Maxwell velocity distribution. Finally, Gibbs, in his book “Elementary principles in statistical mechanics” published in 1902, establishes definitively the equivalence between statistical physics and thermodynamics.

Statistical mechanics is so general that its methods still hold in a much wider context than that on which the original theory was developed. In fact, in spite of its impressive success, considerable efforts have been made in recent years to extend the formalism of statistical mechanics beyond its application limits. Traditional statistical mechanics focuses on systems with many degrees of freedom and becomes exact in the thermodynamic limit. Nevertheless, an increasing amount of physical and physical-like systems known nowadays do not seem to comply with this limit imposed by the large numbers. Often, these systems are characterized by a phase space that self-organizes in a (multi)fractal structure, so that the problem regarding the relationship between statistical and dynamical laws becomes highlighted, since these systems seem to violate the standard ergodic and mixing properties on which the Boltzmann–Gibbs formalism is founded. Definitively, such systems reach a meta-equilibrium configuration that appears better described by a generalized entropic principle different from the traditional Boltzmann–Gibbs form.

The Statistical Mechanics Section, broad and interdisciplinary in scope, intends to present mainly theoretically oriented material (even purely mathematical). It focuses on the challenges of modern statistical mechanics and its applications, while incorporating a high degree of mathematical rigor, in order to provide relevance not only to statistical physicists but also to mathematicians and theoretical physicists interested in interdisciplinary topics. Papers submitted should have real and concrete applications in statistical mechanics or provide clear evidence of possible applications. Papers in pure statistics will not be accepted.

Dr. Antonio M. Scarfone
Section Editor-in-Chief

Keywords

Foundations of classical and quantum statistical mechanics; nonlinear kinetics and related dynamical processes; classical and quantum stochastic processes. Generalizations of statistical mechanics; non-Gibbsian distributions and power–law distributions; non-equilibrium and meta-equilibrium processes. Combinatorial aspects of statistical physics and quantum field theory. Geometric applications (including non-commutative geometry) to statistical physics. Statistical mechanics of complex systems: biological, ecological and evolutionary systems, networks and graphs; collective phenomena in economic and social systems

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