Acceleration of convergence to equilibrium in Markov chains by breaking detailed balance

Johannes Zimmer, Robert Jack, Marcus Kaiser

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We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review existing results showing that irreversible processes converge faster to their steady state than reversible ones. We show how this behaviour appears in the hydrodynamic limit of such processes, as described by macroscopic fluctuation theory, and we provide a quantitative expression for the acceleration of convergence in this setting. We give a geometrical interpretation of this acceleration, in terms of currents that are antisymmetric under time-reversal and orthogonal to the free energy gradient, which act to drive the system away from states where (reversible) gradient-descent dynamics result in slow convergence to equilibrium.
Original languageEnglish
JournalJournal of Statistical Physics
Issue number2
Early online date18 May 2017
Publication statusPublished - 1 Jul 2017


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