Fluctuation relations for anisotropic systems

TL;DR

This paper extends the fluctuation relations for nonequilibrium steady states to anisotropic systems, providing a generalized framework applicable to higher-dimensional, directionally dependent systems, with validation through specific models.

Contribution

It derives a new fluctuation relation for anisotropic $d$-dimensional systems, relaxing the isotropy assumption of previous models.

Findings

Derived a fluctuation relation for anisotropic systems.

Validated the relation using the 2D anisotropic zero-range process.

Applied both exact and hydrodynamic approaches for illustration.

Abstract

Currents of particles or energy in driven nonequilibrium steady states are known to satisfy certain symmetries, referred to as fluctuation relations, determining the ratio of the probabilities of positive fluctuations to negative ones. A generalization of these fluctuation relations has been proposed recently for extended nonequilibrium systems of dimension greater than one, assuming, crucially, that they are isotropic [P. I.\ Hurtado, C.\ P\'erez-Espigares, J. J.\ del Pozo, and P. L.\ Garrido, Proc.\ Nat.\ Acad.\ Sci.\ (USA) \textbf{108}, 7704 (2011)]. Here we relax this assumption and derive a fluctuation relation for $d$-dimensional systems having anisotropic bulk driving rates. We illustrate this anisotropic fluctuation relation for the particle current fluctuations in the 2-$d$ anisotropic zero-range process, using both exact and fluctuating hydrodynamic approaches.