Collective power: Minimal model for thermodynamics of nonequilibrium phase transitions

Tim Herpich, Juzar Thingna, Massimiliano Esposito

Published 2018-02-01Version 1

We establish a direct connection between the linear stochastic dynamics, the nonlinear mean-field dynamics, and the thermodynamic description of a minimal model of driven and interacting discrete oscillators. 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 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. Thermodynamically, the dissipated work of the stochastic dynamics exhibits signatures of nonequilibrium phase transitions over long metastable times which disappear in the infinite-time limit. Remarkably, it is reduced by the attractive interactions between the oscillators. 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 universal linear regime prediction. Our work builds bridges between thermodynamics of nonequilibrium phase transitions and bifurcation theory.