Far-from-equilibrium state in a weakly dissipative model

TL;DR

This paper investigates whether dissipative systems reach equilibrium as dissipation decreases, using a solvable model of energy transfer on a hierarchical tree, revealing a transition to a far-from-equilibrium state at low dissipation.

Contribution

It introduces a simple, solvable model demonstrating a transition from equilibrium to far-from-equilibrium states in low dissipation regimes.

Findings

Transition between quasi-equilibrium and far-from-equilibrium regimes

Far-from-equilibrium state persists even as dissipation approaches zero

Energy transfer dynamics influence the stationary state behavior

Abstract

We address, on the example of a simple solvable model, the issue of whether the stationary state of dissipative systems converges to an equilibrium state in the low dissipation limit. We study a driven dissipative Zero Range Process on a tree, in which particles are interpreted as finite amounts of energy exchanged between degrees of freedom. The tree structure mimicks the hierarchy of length scales; energy is injected at the top of the tree ('large scales'), transferred through the tree and dissipated mostly in the deepest branches of the tree ('small scales'). Varying a parameter characterizing the transfer dynamics, a transition is observed, in the low dissipation limit, between a quasi-equilibrated regime and a far-from-equilibrium one, where the dissipated flux does not vanish.