Gibbs Entropy and Irreversibility

TL;DR

This paper explores how Gibbs entropy relates to irreversibility, extending Onsager theory to phase space, deriving a generalized Liouville equation, and connecting it to the Boltzmann equation.

Contribution

It introduces a phase space extension of Onsager theory, leading to a generalized Liouville equation and insights into the emergence of irreversibility.

Findings

Derivation of a generalized Liouville equation

Connection between Gibbs entropy and irreversibility

Natural emergence of the Boltzmann equation from the formalism

Abstract

This contribution is dedicated to dilucidating the role of the Gibbs entropy in the discussion of the emergence of irreversibility in the macroscopic world from the microscopic level. By using an extension of the Onsager theory to the phase space we obtain a generalization of the Liouville equation describing the evolution of the distribution vector in the form of a master equation. This formalism leads in a natural way to the breaking of the BBGKY hierarchy. As a particular case we derive the Boltzmann equation.