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-towork 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. arXiv:1802.00461v3 [cond-mat.stat-mech]

We study the stochastic dynamics of infinitely many globally interacting units made of q states distributed uniformly along a ring that is externally driven. While repulsive interactions always lead to uniform occupations, attractive interactions give rise to much richer phenomena: We analytically characterize a Hopf bifurcation which separates a high-temperature regime of uniform occupations from a low-temperature one where all units coalesce into a single state. For odd q, below the critical temperature starts a synchronization regime which ends via a second phase transition at lower temperatures, while for even q this intermediate phase disappears. We find that interactions have no effects except below critical temperature for attractive interactions. A thermodynamic analysis reveals that the dissipated work is reduced in this regime, whose temperature range is shown to decrease as q increases. The q-dependence of the power-efficiency trade-off is also analyzed.

We provide a stochastic thermodynamic description across scales for N identical units with allto-all interactions that are driven away from equilibrium by different reservoirs and external forces. We start at the microscopic level with Poisson rates describing transitions between many-body states. We then identify an exact coarse graining leading to a mesoscopic description in terms of Poisson transitions between systems occupations. We also study macroscopic fluctuations using the Martin-Siggia-Rose formalism and large deviation theory. In the macroscopic limit (N → ∞), we derive an exact nonlinear (mean-field) rate equation describing the deterministic dynamics of the most likely occupations. Thermodynamic consistency, in particular the detailed fluctuation theorem, is demonstrated across microscopic, mesoscopic and macroscopic scales. The emergent notion of entropy at different scales is also outlined. Macroscopic fluctuations are calculated semianalytically in an out-of-equilibrium Ising model. Our work provides a powerful framework to study thermodynamics of nonequilibrium phase transitions.

Starting from the stochastic thermodynamics description of two coupled underdamped Brownian particles, we showcase and compare three different coarse-graining schemes leading to an effective thermodynamic description for the first of the two particles: Marginalization over one particle, bipartite structure with information flows and the Hamiltonian of mean force formalism. In the limit of time-scale separation where the second particle locally equilibrates, the effective thermodynamics resulting from the first and third approach is shown to capture the full thermodynamics and to coincide with each other. In the bipartite approach, the slow part does not, in general, allow for an exact thermodynamic description as the entropic exchange between the particles is ignored. Physically, the second particle effectively becomes part of the heat reservoir. In the limit where the second particle becomes heavy and thus deterministic, the effective thermodynamics of the first two coarse-graining methods coincides with the full one. The Hamiltonian of mean force formalism however is shown to be incompatible with that limit. Physically, the second particle becomes a work source. These theoretical results are illustrated using an exactly solvable harmonic model.

We investigate the performance of majority-logic decoding in both reversible and finite-time information erasure processes performed on macroscopic bits that contain N microscopic binary units. While we show that for reversible erasure protocols single-unit transformations are more efficient than majority-logic decoding, the latter is found to offer several benefits for finite-time erasure processes: Both the minimal erasure duration for a given erasure and the minimal erasure error for a given erasure duration are reduced, if compared to a single unit. Remarkably, the majority-logic decoding is also more efficient in both the small erasure error and fast erasure region. These benefits are also preserved under the optimal erasure protocol that minimizes the dissipated heat. Our work therefore shows that majority-logic decoding can lift the precision-speed-efficiency trade-off in information erasure processes.