A low temperature analysis of the boundary driven Kawasaki Process

TL;DR

This paper analyzes the dominant states of a one-dimensional diffusive lattice gas at low temperatures, revealing a complex phase diagram influenced by interactions and chemical potentials, with implications for nonequilibrium systems.

Contribution

It provides a detailed low temperature analysis of the boundary driven Kawasaki process, identifying dominant states and their dependence on system parameters.

Findings

Dominant states do not correspond to lowest energy configurations.

The phase diagram depends critically on interaction strength and chemical potentials.

Dynamical activity decreases with temperature, affecting state accessibility.

Abstract

Low temperature analysis of nonequilibrium systems requires finding the states with the longest lifetime and that are most accessible from other states. We determine these dominant states for a one-dimensional diffusive lattice gas subject to exclusion and with nearest neighbor interaction. They do not correspond to lowest energy configurations even though the particle current tends to zero as the temperature reaches zero. That is because the dynamical activity that sets the effective time scale, also goes to zero with temperature. The result is a non-trivial asymptotic phase diagram, which crucially depends on the interaction coupling and the relative chemical potentials of the reservoirs.