Non-equilibrium phase coexistence in boundary-driven diffusive systems

TL;DR

This paper investigates liquid-gas phase coexistence in boundary-driven diffusive systems, revealing how interface width influences the phase behavior and introducing a new variational principle for the density profile.

Contribution

It introduces a novel variational principle for phase coexistence in non-equilibrium systems, extending thermodynamics to boundary-driven diffusive systems with varying interface widths.

Findings

Phase coexistence condition aligns with local equilibrium thermodynamics when interface width is large.

A new variational principle determines the most probable density profile for small interface widths.

Numerical simulations confirm the theoretical predictions.

Abstract

Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is much larger than $\Lambda$, the discrete model becomes the standard fluctuating hydrodynamics, where the phase coexistence condition is given by the local equilibrium thermodynamics. In contrast, when $\ell < \Lambda$, the most probable density profile is determined by a new variational principle, where the chemical potential at the interface is found to deviate from the equilibrium coexistence chemical potential. This means that metastable states at equilibrium stably appear near the interface as the influence of the particle current. The variational function derived in the theoretical analysis is also found to be equivalent to the variational function formulated in an extended framework of thermodynamics called global thermodynamics. Finally, the validity of the theoretical result is confirmed by numerical simulations.