Mesoscopic virial equation for nonequilibrium statistical mechanics

TL;DR

This paper develops mesoscopic virial equations applicable to various nonequilibrium steady states, enabling the derivation of state equations that incorporate heat flows and dissipation in stochastic and deterministic systems.

Contribution

It introduces a new class of virial equations for nonequilibrium systems, extending to collective modes and providing a framework for nonequilibrium state equations.

Findings

Virial equations apply to Langevin and Nosé–Hoover dynamics.

Derived nonequilibrium state equations involving heat flows.

Extended virial theorem to collective modes in heat-conducting lattices.

Abstract

We derive a class of mesoscopic virial equations governing energy partition between conjugate position and momentum variables of individual degrees of freedom. They are shown to apply to a wide range of nonequilibrium steady states with stochastic (Langevin) and deterministic (Nos\'e--Hoover) dynamics, and to extend to collective modes for models of heat-conducting lattices. A generalised macroscopic virial theorem ensues upon summation over all degrees of freedom. This theorem allows for the derivation of nonequilibrium state equations that involve dissipative heat flows on the same footing with state variables, as exemplified for inertial Brownian motion with solid friction and overdamped active Brownian particles subject to inhomogeneous pressure.