Non-equilibrium 2D Ising model with stationary uphill diffusion

TL;DR

This paper demonstrates that uphill diffusion, typically observed in multicomponent systems, can occur in a single-component 2D Ising model under non-equilibrium conditions with external work, revealing new steady-state behaviors.

Contribution

It provides numerical evidence of uphill diffusion in a single-component 2D Ising model driven by boundary reservoirs, linking equilibrium magnetization to non-equilibrium current behavior.

Findings

Existence of non-equilibrium steady states with uphill diffusion.

Current changes from downhill to uphill as reservoir magnetizations are tuned.

Current vanishes when reservoir magnetizations match equilibrium magnetization.

Abstract

Usually, in a non-equilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e. it may occur even in single component systems as a consequence of some external work. To this aim we consider the 2D ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs. We provide numerical evidence that a class of non-equilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such non-equilibrium set-up, the current vanishes precisely when the reservoir magnetizations equal the magnetization of the corresponding equilibrium dynamics, thus establishing a novel relation between equilibrium and non-equilibrium properties.