Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study

TL;DR

This study uses kinetic Monte Carlo simulations to analyze current fluctuations in boundary driven diffusive systems across various dimensions, confirming theoretical predictions and revealing dimension-dependent behaviors.

Contribution

It provides a numerical validation of the additivity principle and macroscopic fluctuation theory for current fluctuations in different dimensions.

Findings

Current fluctuations agree with theoretical predictions.

Current distribution is shape-independent for macroscopic contacts.

Dimension influences the current statistics, except for specific processes.

Abstract

We use kinetic Monte Carlo simulations to investigate current fluctuations in boundary driven generalized exclusion processes, in different dimensions. Simulation results are in full agreement with predictions based on the additivity principle and the macroscopic fluctuation theory. The current statistics are independent of the shape of the contacts with the reservoirs, provided they are macroscopic in size. In general, the current distribution depends on the spatial dimension. For the special cases of the symmetric simple exclusion process and the zero-range process, the current statistics are the same for all spatial dimensions.