Shape-Dependent Thermodynamics and Non-Local Hydrodynamics in a Non-Gibbsian Steady-State of a Drift-Diffusion System

TL;DR

This paper demonstrates that driven diffusive systems exhibit shape-dependent thermodynamics and non-local hydrodynamics in steady states, which are supported by simulations and involve non-Gibbsian measures due to long-range interactions.

Contribution

It reveals the presence of shape-dependent thermodynamics and non-local hydrodynamics in non-Gibbsian steady states of driven systems, supported by numerical evidence.

Findings

Shape-dependent thermodynamics confirmed by simulations

Non-local hydrodynamics observed in steady states

Invariant measures are non-Gibbsian due to long-range potentials

Abstract

Shape-dependent thermodynamics and non-local hydrodynamics are argued to occur in dissipative steady states of driven diffusive systems. These predictions are confirmed by numerical simulations. Unlike power-law correlations, these phenomena cannot be explained by a hypothesis of ``criticality''. Instead, they require the effective Hamiltonian of the system to contain very long-range potentials, making the invariant probability measures formally ``non-Gibbsian''.