Collective power: Minimal model for thermodynamics of nonequilibrium phase transitions

TL;DR

This paper introduces a minimal thermodynamically consistent model for nonequilibrium phase transitions involving synchronization, revealing how metastability and interactions influence work dissipation and efficiency in driven, interacting three-state units.

Contribution

It presents a novel minimal model combining thermodynamics and bifurcation theory to analyze nonequilibrium phase transitions and synchronization phenomena.

Findings

Dissipated work decreases with attractive interactions.

Maximum power occurs far from equilibrium in the synchronization phase.

Efficiency at maximum power is close to linear response predictions.

Abstract

We propose a thermodynamically consistent minimal model to study synchronization which is made of driven and interacting three-state units. This system exhibits at the mean-field level two bifurcations separating three dynamical phases: a single stable fixed point, a stable limit cycle indicative of synchronization, and multiple stable fixed points. These complex emergent dynamical behaviors are understood at the level of the underlying linear Markovian dynamics in terms of metastability, i.e. the appearance of gaps in the upper real part of the spectrum of the Markov generator. Stochastic thermodynamics is used to study the dissipated work across dynamical phases as well as across scales. This dissipated work is found to be reduced by the attractive interactions between the units and to nontrivially depend on the system size. When operating as a work-to-work converter, we find that the maximum power output is achieved far-from-equilibrium in the synchronization regime and that the efficiency at maximum power is surprisingly close to the linear regime prediction. Our work shows the way towards building a thermodynamics of nonequilibrium phase transitions in conjunction to bifurcation theory.