On the Statistical Foundations of Irreversible Thermodynamics

Abstract

We briefly, and partially, consider aspects of the present status of phenomenological irreversible thermodynamics and nonequilibrium statistical mechanics. After short comments on Classical Irreversible Thermodynamics, its conceptual and practical shortcomings are pointed out, as well as the efforts undertaken to go beyond its limits, consisting of particular approaches to a more general theory of Irreversible Thermodynamics. In particular, a search for statistical‐mechanical foundations of Irreversible Thermodynamics, namely, the construction of a statistical thermodynamics, are based on the Non‐equilibrium Statistical Operator Method. This important theory for the treatment of phenomena at the macroscopic level, is based on a microscopic molecular description in the context of a nonequilibrium ensemble formalism. We draw attention to the fact that this method may be considered to be emcompassed within Jaynes' Predictive Statistical Mechanics and based on the principle of maximization of informational entropy. Finally, we describe how, in fact, the statistical method provides foundations to phenomenological irreversible thermodynamics, thus giving rise to what can be referred to as Informational Statistical Thermodynamics.

Numerical analysis of the relaxation of photoexcited carriers and the hot-phonon effect in GaN

“…The process of hot-carriers' cooling in semiconductors, excited by a laser pulse, is one of the most important processes in the field of nonequilibrium transport phenomena, as it involves a combination of many-body physics and statistical mechanics of irreversible processes and its study has achieved noticeable progress in recent years [22][23][24][25].…”

“…The MaxEnt-NESOM can be considered as an advanced generalization of statistical formalisms based on Boltzmann and Gibbs' fundamental ideas and seems to offer a very practical treatment in the theory of irreversible processes. The MaxEnt-NESOM is based on Bogoliubov principle [22][23][24]29] that in general there exists a hierarchy of relaxation t m times such that as time goes on the system keeps losing memory of the initial distribution, so that an ever decreasing number of variables is enough for the description of the system macroscopic state. This contraction is connected with the separation from the total Hamiltonian of strong interactions with certain symmetries (interactions related to the fast relaxing processes).…”

“…This contraction is connected with the separation from the total Hamiltonian of strong interactions with certain symmetries (interactions related to the fast relaxing processes). In the contracted description, the macroscopic state of the system is characterized by a reduced set of thermodynamic variables, say Q j ðtÞ with j ¼ 1; 2; y; n; which are the average values in accordance with the nonequilibrium statistical operator rðtÞ of a corresponding set of dynamical variables P j : Application of this method to the investigation of the highly photo-excited semiconductor was reported in detail in previous papers [2][3][4]23], and here we shall proceed directly to use those equations. Following Refs.…”

“…Following Refs. [2][3][4]23] we must choose a basic set of dynamical variables that characterizes the macroscopic state of the system composed by…”

“…(7) the nonequilibrium statistical operator rðtÞ; constructed resorting to the Jaynes' principle of maximization of the statistical-information entropy (MaxEnt) [22][23][24] can be separated (details are given in Refs. [22][23][24]) into two parts, namely, rðtÞ ¼ % rðt; 0Þ þ r 0 ðtÞ: Here % r is an instantaneous (in time) Gibbs-like (coarse-grained) distribution, which defines the average values of quantities P j at time t; that is…”