Minimum-dissipation principle for synchronized stochastic oscillators far from equilibrium.

We prove a linear stability-dissipation relation (SDR) for q-state Potts models driven far from equilibrium by a nonconservative force. At a critical coupling strength, these models exhibit a synchronization transition from a decoherent into a synchronized state. In the vicinity of this transition, the SDR connects the entropy production rate per oscillator to the phase-space contraction rate, a measure of stability, in a simple way.

Small-amplitude synchronization in driven Potts models.

We study driven q-state Potts models with thermodynamically consistent dynamics and global coupling. For a wide range of parameters, these models exhibit a dynamical phase transition from decoherent oscillations into a synchronized phase. Starting from a general microscopic dynamics for individual oscillators, we derive the normal form of the high-dimensional Hopf bifurcation that underlies the phase transition.

Finite-Time Dynamical Phase Transition in Nonequilibrium Relaxation.

We uncover a finite-time dynamical phase transition in the thermal relaxation of a mean-field magnetic model. The phase transition manifests itself as a cusp singularity in the probability distribution of the magnetization that forms at a critical time. The transition is due to a sudden switch in the dynamics, characterized by a dynamical order parameter.

Relaxation-speed crossover in anharmonic potentials.

In a recent Letter [A. Lapolla and A. Godec, Phys.

Heavy particles in a persistent random flow with traps.

We study a one-dimensional model for heavy particles in a compressible fluid. The fluid-velocity field is modeled by a persistent Gaussian random function, and the particles are assumed to be weakly inertial. Since one-dimensional fluid-velocity fields are always compressible, the model exhibits spatial trapping regions where particles tend to accumulate.