Nonequilibrium thermodynamics and Nose-Hoover dynamics

TL;DR

This paper develops a consistent nonequilibrium thermodynamics framework for systems driven by external forces under Nose-Hoover dynamics, linking entropy production to system-reservoir correlations.

Contribution

It introduces a thermodynamic description for Nose-Hoover systems with initial canonical equilibrium, connecting entropy production to relative entropy.

Findings

Entropy production equals relative entropy of system-reservoir correlations.

First and second laws are established for Nose-Hoover driven systems.

Reservoir treated as thermostatted variable initially in equilibrium.

Abstract

We show that systems driven by an external force and described by Nose-Hoover dynamics allow for a consistent nonequilibrium thermodynamics description when the thermostatted variable is initially assumed in a state of canonical equilibrium. By treating the "real" variables as the system and the thermostatted variable as the reservoir, we establish the first and second law of thermodynamics. As for Hamiltonian systems, the entropy production can be expressed as a relative entropy measuring the system-reservoir correlations established during the dynamics.