Spatial fluctuation theorem

TL;DR

This paper introduces a new fluctuation relation for non-equilibrium systems with spatial symmetries, linking probabilities of different directional currents, and extends the Gallavotti-Cohen theorem to spatial observables.

Contribution

It derives a novel fluctuation relation based on spatial symmetries, generalizing existing time-reversal based theorems for vectorial observables.

Findings

Establishes a quantitative relation between directional current probabilities.

Generalizes the Gallavotti-Cohen fluctuation theorem to spatial symmetries.

Suggests potential for experimental measurement of spatial fluctuation relations.

Abstract

For non-equilibrium systems of interacting particles and for interacting diffusions in d dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.