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Abstract

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
Volume168
Issue number2
Early online date18 May 2017
DOIs
Publication statusPublished - 1 Jul 2017

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Acceleration of Convergence
Convergence to Equilibrium
Hydrodynamic Limit
Detailed Balance
Markov chains
Markov chain
Fluctuations (theory)
Irreversible Processes
Interacting Particle Systems
Scaling Limit
Time Reversal
Gradient Descent
Antisymmetric
hydrodynamics
Free Energy
fluctuation theory
gradients
irreversible processes
descent
Gradient

Cite this

Acceleration of convergence to equilibrium in Markov chains by breaking detailed balance. / Zimmer, Johannes; Jack, Robert; Kaiser, Marcus.

In: Journal of Statistical Physics, Vol. 168, No. 2, 01.07.2017.

Research output: Contribution to journalArticle

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