Vortices in the two-dimensional Simple Exclusion Process

TL;DR

This paper demonstrates that vortices dominate partial current fluctuations in 2D diffusive systems, causing a different scaling than hydrodynamic predictions, supported by exact calculations and simulations for the symmetric simple exclusion process.

Contribution

It reveals the role of vortices in current fluctuations and provides exact variance computations for the symmetric simple exclusion process on general graphs.

Findings

Vortices lead to a logarithmic system size dependence of partial flux fluctuations.

Exact variance expressions are derived for the symmetric simple exclusion process.

Numerical simulations confirm the theoretical predictions.

Abstract

We show that the fluctuations of the partial current in two dimensional diffusive systems are dominated by vortices leading to a different scaling from the one predicted by the hydrodynamic large deviation theory. This is supported by exact computations of the variance of partial current fluctuations for the symmetric simple exclusion process on general graphs. On a two-dimensional torus, our exact expressions are compared to the results of numerical simulations. They confirm the logarithmic dependence on the system size of the fluctuations of the partialflux. The impact of the vortices on the validity of the fluctuation relation for partial currents is also discussed.