Nonequilibrium statistical mechanics and entropy production in a classical infinite system of rotators

TL;DR

This paper investigates entropy production in an infinite classical system of coupled rotators driven out of equilibrium by external forces or temperature differences, analyzing various definitions and their bounds.

Contribution

It introduces and compares multiple definitions of entropy production in an infinite Hamiltonian system, establishing their consistency with thermodynamic expectations.

Findings

Entropy production bounds are consistent with thermostat temperatures.

Different definitions of entropy production satisfy expected thermodynamic bounds.

The analysis applies to both energy injection and heat flow scenarios.

Abstract

We analyze the dynamics of a simple but nontrivial classical Hamiltonian system of infinitely many coupled rotators. We assume that this infinite system is driven out of thermal equilibrium either because energy is injected by an external force (Case I), or because heat flows between two thermostats at different temperatures (Case II). We discuss several possible definitions of the entropy production associated with a finite or infinite region, or with a partition of the system into a finite number of pieces. We show that these definitions satisfy the expected bounds in terms of thermostat temperatures and energy flow.