Parallel Temperature Interfaces in the Katz-Lebowitz-Spohn Driven Lattice Gas

TL;DR

This study investigates a two-region driven lattice gas with different temperatures, revealing how temperature boundaries influence particle fluctuations, current flow, and entropy production, with critical behavior emerging under specific conditions.

Contribution

It introduces a novel two-temperature lattice gas model with particle-hole symmetry at interfaces, analyzing finite-size scaling and critical phenomena in driven nonequilibrium systems.

Findings

Particle density fluctuations follow KLS critical exponents when one region is critical.

Interface currents can suppress particle exchange, leading to subsystem decoupling.

Entropy production exhibits algebraic decay at criticality and saturation at high temperatures.

Abstract

We explore a variant of the Katz-Lebowitz-Spohn (KLS) driven lattice gas in two dimensions, where the lattice is split into two regions that are coupled to heat baths with distinct temperatures. The temperature boundaries are oriented parallel to the external particle drive. If the hopping rates at the interfaces satisfy particle-hole symmetry, the current difference across them generates a vector flow diagram akin to a vortex sheet. We have studied the finite-size scaling of the particle density fluctuations in both temperature regions, and observed that it is controlled by the respective temperature values. If the colder subsystem is maintained at the KLS critical temperature, while the hotter subsystem's temperature is set much higher, the interface current greatly suppresses particle exchange between the two regions. As a result of the ensuing effective subsystem decoupling, strong fluctuations persist in the critical region, whence the particle density fluctuations scale with the KLS critical exponents. However, if both temperatures are set well above the critical temperature, the particle density fluctuations scale according to the totally asymmetric exclusion process (TASEP). We have also measured the entropy production rate in both subsystems; it displays intriguing algebraic decay in the critical region, while it saturates quickly at a small but non-zero level in the hotter region. We have also considered another possible choice of the hopping rates across the temperature interfaces that explicitly breaks particle-hole symmetry. In that case the boundary rates induce a net particle flux across the interfaces that displays power-law behavior, until ultimately the particle exclusion constraints generate a clogging transition to an inert state.