A general theory for irreversible thermodynamics

TL;DR

This paper presents a unified framework for irreversible thermodynamics, showing how irreversibility, the second law, and fluctuation theorems emerge from microscopic reversibility and memory effects in individual system pathways.

Contribution

It introduces a general theory linking microscopic reversibility and non-Markovian memory to macroscopic irreversibility and thermodynamic laws.

Findings

Derives known fluctuation theorems from microscopic principles

Shows second law arises from microscopic reversibility and memory

Unifies non-equilibrium statistics under a common framework

Abstract

We demonstrate that irreversibility arises from the principle of microscopic reversibility and the presence of memory in the time evolution of a single copy of a system driven by a protocol. We introduce microscopic reversibility by using the concept of protocol- and pathway-dependent thermodynamic function, as defined in J.R. Arias-Gonzalez, arXiv:1511.08017 [cond-mat.stat-mech], and memory by using the concept of non-Markovianity, as in J.R. Arias-Gonzalez, arXiv:1511.06139 [cond-mat.stat-mech]. We define work as the change in free energy and heat as the change in entropy for micoscopic, individual pathways of a system subject to a protocol. We find that all non-equilibrium statistics emerge naturally. In particular, we derive most known fluctuation theorems and formulate two others. While the conservation of energy is invoked both at the level of the individual pathway and in ensemble-average processes, the second law of thermodynamics and the time arrow, which are only fulfilled in ensemble-average processes, are shown to be consequences of microscopic reversibility and non-Markovianity.