Minimal entropy production in the presence of anisotropic fluctuations

TL;DR

This paper investigates the minimal entropy production in anisotropic thermodynamic systems, revealing that anisotropy complicates entropy minimization and linking it to a modified optimal transport problem, with implications for biological processes.

Contribution

It introduces a modified optimal mass transport framework to characterize minimal entropy production in anisotropic environments, accounting for non-conservative forces and steady-state seepage.

Findings

Entropy production can be expressed via a modified OMT problem in anisotropic settings.

Maintaining non-equilibrium steady states incurs intrinsic entropic costs.

Anisotropy prevents entropy from being zero when the thermodynamic state is unchanged.

Abstract

Anisotropy in temperature, chemical potential, or ion concentration, provides the fuel that feeds dynamical processes that sustain life. At the same time, anisotropy is a root cause of incurred losses manifested as entropy production. In this work we consider a rudimentary model of an overdamped stochastic thermodynamic system in an anisotropic temperature heat bath, and study minimum entropy production when driving the system between thermodynamic states in finite time. While entropy production in isotropic temperature environments can be expressed in terms of the length (in the Wasserstein-2 metric) traversed by the thermodynamic state of the system, anisotropy complicates substantially the mechanism of entropy production since, besides dissipation, seepage of energy between ambient anisotropic heat sources by way of the system dynamics is often a major contributing factor. A key result of the paper is to show that in the presence of anisotropy, minimization of entropy production can once again be expressed via a modified Optimal Mass Transport (OMT) problem. However, in contrast to the isotropic situation that leads to a classical OMT problem and a Wasserstein length, entropy production may not be identically zero when the thermodynamic state remains unchanged (unless one has control over non-conservative forces); this is due to the fact that maintaining a Non-Equilibrium Steady-State (NESS) incurs an intrinsic entropic cost that can be traced back to a seepage of heat between heat baths. As alluded to, NESSs represent hallmarks of life, since living matter by necessity operates far from equilibrium. Therefore, the question studied herein, to characterize minimal entropy production in anisotropic environments, appears of central importance in biological processes and on how such processes may have evolved to optimize for available usage of resources.