Weakly Non-Equilibrium Properties of Symmetric Inclusion Process with Open Boundaries

TL;DR

This paper investigates the near-equilibrium behavior of the one-dimensional Symmetric Inclusion Process with open boundaries, deriving the first-order non-equilibrium correction and showing it aligns with local equilibrium measures.

Contribution

It provides an explicit calculation of the McLennan ensemble for SIP, revealing the structure of the first-order correction as a product measure.

Findings

First-order correction is a product measure.

Correction aligns with local equilibrium measure.

Weak particle current induced by boundary reservoirs.

Abstract

We study close to equilibrium properties of the one-dimensional Symmetric Inclusion Process (SIP) by coupling it to two particle-reservoirs at the two boundaries with slightly different chemical potentials. The boundaries introduce irreversibility and induce a weak particle current in the system. We calculate the McLennan ensemble for SIP, which corresponds to the entropy production and the first order non-equilibrium correction for the stationary state. We find that the first order correction is a product measure, and is consistent with the local equilibrium measure corresponding to the steady state density profile.