Submitted Abstract
A first key achievement of this research project has been the publication of the paper :Tim Herpich, Juzar Thingna, and Massimiliano EspositoPhys. Rev. X 8, 031056 (2018)In this paper 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 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 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.Another work that will be published soon generalizes the three-state units to q-state units and reveals that there are two (thermo)dynamical universality classes dependent on whether q is even or odd. Furthermore, we reconfirm for any q that the work dissipated by the units is reduced for any finite attractive interactions. Finally, it is demonstrated that the efficiency at maximum power is achieved in the synchronization regime also for q>3. While the generated power increases with q, the associated efficiency is decreased suggesting that the efficiency-power trade-off is not lifted by changing the topology of the synchronized system.