Minimum-dissipation principle for synchronised stochastic oscillators far from equilibrium

Abstract

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 synchronisation transition from a decoherent into a synchronised 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. For large but finite systems, we argue that the SDR implies a minimum-dissipation principle for driven Potts models as the dynamics selects stable non-equilibrium states with least dissipation. This principle holds arbitrarily far from equilibrium, for any stochastic dynamics, and for all $q$.

6 pages, 4 figures, 3 supplemental videos

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