System driven out-of equilibrium by weak contacts with reservoirs

TL;DR

This paper explores how the dimension and contact geometry influence non-equilibrium particle systems driven by reservoirs, revealing different regimes and proposing extensions to fluctuation theory for mesoscopic contacts.

Contribution

It investigates the effects of dimension and contact geometry on non-equilibrium regimes and extends macroscopic fluctuation theory for mesoscopic reservoirs.

Findings

In 2D, three regimes depend on coupling strength, similar to 1D.

In 3D and higher, only a weak coupling regime exists.

Macroscopic fluctuation theory applies to mesoscopic reservoir contacts.

Abstract

The non-equilibrium behavior of particle systems driven by reservoirs has been extensively studied in recent years. In one dimension, various regimes have been explored depending on the coupling strength to the reservoirs. In this paper, we investigate the role of the dimension and of the geometry of the contacts with the reservoirs. For the symmetric simple exclusion process with point contact reservoirs, we show that in dimension 2, as in one dimension, three different regimes occur depending on the coupling strength. On the other hand in dimensions 3 and higher, there exists only a weak coupling regime which is very sensitive to the microscopic structure of the contacts. We then argue that for reservoirs with mesoscopic size contacts the macroscopic fluctuation theory remains in force and we propose an extension of the additivity principle for multiple mesoscopic reservoirs.