Two extensions of exact non-equilibrium steady states of a boundary driven cellular automaton

TL;DR

This paper extends the exact solutions of non-equilibrium steady states in a boundary-driven cellular automaton by generalizing boundary conditions, revealing two new solvable cases with potential applications in statistical physics.

Contribution

It introduces two novel extensions of existing exact steady state solutions by modifying boundary conditions and incorporating conserved quantities as energy reservoirs.

Findings

Two new solvable cases of steady states identified

Generalized boundary conditions lead to exact solutions

Original solution is a special case of the new framework

Abstract

Recently Prosen and Mej\'ia-Monasterio (J. Phys. A: Math. Theor. 49 (2016) 185003) obtained exact nonequilibrium steady states of an integrable and reversible cellular automaton driven by some stochastic boundary conditions. In this paper, we explore the possible extensions of their method by generalizing the boundary conditions. As the result, we find two cases where such an extension is possible. One is the case where a special condition is satisfied in a generalized boundary condition. The other is obtained by considering a conserved quantity as energy and boundaries as heat reservoirs. The latter includes the original solution as the special case. Properties of the both solutions are discussed.