Persistent energy flow for a stochastic wave equation model in nonequilibrium statistical mechanics

TL;DR

This paper studies a stochastic wave equation model in nonequilibrium statistical mechanics, demonstrating persistent energy flow around a ring even without bath interactions, with implications for heat transfer in complex systems.

Contribution

It introduces a novel stochastic PDE model combining wave dynamics and heat baths, showing persistent energy flow in nonequilibrium conditions.

Findings

Energy flow persists without bath interaction in a linear field.

A simple example illustrates the persistent energy flow phenomenon.

The model bridges wave equations and stochastic heat transfer in nonequilibrium systems.

Abstract

We consider a one-dimensional partial differential equation system modeling heat flow around a ring. The system includes a Klein-Gordon wave equation for a field satisfying spatial periodic boundary conditions, as well as Ornstein-Uhlenbeck stochastic differential equations with finite rank dissipation and stochastic driving terms modeling heat baths. There is an energy flow around the ring. In the case of a linear field with different (fixed) bath temperatures, the energy flow can persist even when the interaction with the baths is turned off. A simple example is given.