TL;DR: In this paper, the fundamentals conditions for equilibrium and stability of non-equilibrium systems are defined. And the Monte Carlo method in statistical mechanics is used for non-interacting (ideal) systems.
Abstract: Thermodynamics, fundamentals conditions for equilibrium and stability statistical mechanics non-interacting (ideal) systems statistical mechanical theory of phase transitions Monte Carlo method in statistical mechanics classical fluids statistical mechanics of non-equilibrium systems.
TL;DR: In this article, the Boltzmann-Gibbs Statistical Mechanics (BSM) theory is generalized to nonextensive statistical mechanics and applied in thermodynamic and non-thermodynamic applications.
Abstract: Basics or How the Theory Works.- Historical Background and Physical Motivations.- Learning with Boltzmann-Gibbs Statistical Mechanics.- Generalizing What We Learnt: Nonextensive Statistical Mechanics.- Foundations or Why the Theory Works.- Stochastic Dynamical Foundations of~Nonextensive Statistical Mechanics.- Deterministic Dynamical Foundations of Nonextensive Statistical Mechanics.- Generalizing Nonextensive Statistical Mechanics.- Applications or What for the Theory Works.- Thermodynamical and Nonthermodynamical Applications.- Last (But Not Least).- Final Comments and Perspectives.
TL;DR: In this article, the relation between nonequilibrium statistical mechanics and ergodic theory has been studied, and a notation for discussing finite systems of classical point particles has been established.
Abstract: We begin with some very general and elementary remarks about nonequilibrium statistical mechanics. We then establish our notation for discussing finite systems of classical point particles, construct the microcanonical ensemble, and sketch some of the relations between statistical mechanics and ergodic theory.