### Abstract

Original language | English |
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Journal | Journal of Statistical Physics |

Volume | 168 |

Issue number | 2 |

Early online date | 18 May 2017 |

DOIs | |

Publication status | Published - 1 Jul 2017 |

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### Cite this

*Journal of Statistical Physics*,

*168*(2). https://doi.org/10.1007/s10955-017-1805-z

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

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 168, no. 2. https://doi.org/10.1007/s10955-017-1805-z

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TY - JOUR

T1 - Acceleration of convergence to equilibrium in Markov chains by breaking detailed balance

AU - Zimmer, Johannes

AU - Jack, Robert

AU - Kaiser, Marcus

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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.

AB - 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.

U2 - 10.1007/s10955-017-1805-z

DO - 10.1007/s10955-017-1805-z

M3 - Article

VL - 168

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2

ER -