Temperature in nonequilibrium systems with conserved energy

TL;DR

This paper investigates nonequilibrium lattice models with conserved energy, defining a temperature analogous to equilibrium, and finds that their macroscopic behavior can be described by a two-parameter model, despite differences in fluctuation-dissipation relations.

Contribution

The study introduces an analytical solution for a subclass of nonequilibrium models and proposes a two-parameter framework for their macroscopic properties.

Findings

Defined a temperature T_{th} in nonequilibrium systems.

Found a linear fluctuation-dissipation relation with a different slope from T_{th}^{-1}.

Numerical renormalization suggests universal coarse-grained behavior.

Abstract

We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing to define a temperature T_{th} along the same lines as in the equilibrium microcanonical ensemble. The fluctuation-dissipation relation is explicitely found to be linear, but its slope differs from the inverse temperature T_{th}^{-1}. A numerical renormalization group procedure suggests that, at a coarse-grained level, all models behave similarly, leading to a two-parameter description of their macroscopic properties.