Universal current fluctuations in the symmetric exclusion process and other diffusive systems

TL;DR

This paper demonstrates that the current fluctuations in the symmetric simple exclusion process are universal across different dimensions and domains, supported by numerical evidence and theoretical analysis.

Contribution

It extends the macroscopic fluctuation theory to show universality of current statistics in diffusive systems across arbitrary dimensions and geometries.

Findings

Current fluctuations are dimension-independent for SSEP on large domains.

Numerical results support universality in squares, with some discrepancies in cubes.

Increasing contact size may reconcile differences in higher dimensions.

Abstract

We show, using the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim, that the statistics of the current of the symmetric simple exclusion process (SSEP) connected to two reservoirs are the same on an arbitrary large finite domain in dimension $d$ as in the one dimensional case. Numerical results on squares support this claim while results on cubes exhibit some discrepancy. We argue that the results of the macroscopic fluctuation theory should be recovered by increasing the size of the contacts. The generalization to other diffusive systems is straightforward.