Exponential rate of convergence in current reservoirs

TL;DR

This paper investigates a family of particle systems modeling current reservoirs and Fick's law, demonstrating that their convergence to equilibrium occurs at an exponential rate proportional to the inverse square of the system size.

Contribution

It establishes the exponential convergence rate of these particle systems to stationarity as proportional to N^{-2}, providing a rigorous mathematical result for current reservoirs.

Findings

Convergence rate is of order N^{-2}.

Exponential convergence to stationary measure proven.

Model aligns with physical laws like Fick's law.

Abstract

In this paper, we consider a family of interacting particle systems on $[-N,N]$ that arises as a natural model for current reservoirs and Fick's law. We study the exponential rate of convergence to the stationary measure, which we prove to be of the order $N^{-2}$.