Time-Reversal and Entropy

TL;DR

This paper explores the fundamental connection between entropy production and time-reversal symmetry breaking in thermodynamic processes, providing a mathematical framework applicable to both closed and open systems.

Contribution

It offers a unified mathematical explanation linking entropy production, phase-space contraction, and time-reversal symmetry breaking, including a general algorithm for computing entropy production.

Findings

Identifies entropy production as the source of time-reversal symmetry breaking.

Provides a general method to compute entropy production from microscopic dynamics.

Discusses the role of the Markov approximation in thermodynamic descriptions.

Abstract

There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations between entropy production, phase-space contraction and time-reversal starting from a deterministic dynamics. Both closed and open systems, in the transient and in the steady regime, are considered. The main result identifies under general conditions the statistical mechanical entropy production as the source term of time-reversal breaking in the path space measure for the evolution of reduced variables. This provides a general algorithm for computing the entropy production and to understand in a unified way a number of useful (in)equalities. We also discuss the Markov approximation. Important are a number of old theoretical ideas for connecting the microscopic dynamics with thermodynamic behavior.