Thermal response in driven diffusive systems

TL;DR

This paper develops a method to evaluate the linear thermal response of driven nonequilibrium systems with Langevin dynamics, addressing the challenges posed by temperature-dependent noise and providing a stable numerical approach.

Contribution

It introduces a fluctuation-based algorithm for thermal susceptibility in driven systems, overcoming ultraviolet issues and enabling stable, fine-resolution simulations.

Findings

Derived a fluctuation expression for thermal susceptibility.

Developed a stable numerical algorithm for response evaluation.

Validated the approach with fine-resolution simulations.

Abstract

Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast relaxing mechanical, chemical or thermal equilibrium reservoirs. Modifying one of the temperatures creates both entropy fluxes and changes in dynamical activity. That is not unlike mechanical response of nonequilibrium systems but the extra difficulty for perturbation theory via path-integration is that for a Langevin dynamics temperature also affects the noise amplitude and not only the drift part. Using a discrete-time mesh adapted to the numerical integration one avoids that ultraviolet problem and we arrive at a fluctuation expression for its thermal susceptibility. The algorithm appears stable under taking even finer resolution.