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

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 \emph{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.

27 pages, 8 figures

References in corpus (9)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuations and response of nonequilibrium states
• Accelerating diffusions
• Irreversible Langevin samplers and variance reduction: a large deviation approach
• Improving the convergence of reversible samplers
• Improving the Asymptotic Performance of Markov Chain Monte-Carlo by Inserting Vortices
• Eigenvalue analysis of an irreversible random walk with skew detailed balance conditions
• Geometrical interpretation of fluctuating hydrodynamics in diffusive systems

Cited by in corpus (16)

• Topological localization in out-of-equilibrium dissipative systems
• Canonical structure and orthogonality of forces and currents in irreversible Markov chains
• Characterising the nonequilibrium stationary states of Ornstein-Uhlenbeck processes
• Sampling efficiency of transverse forces in dense liquids
• Role of current fluctuations in nonreversible samplers
• Efficient Irreversible Monte Carlo samplers
• Thermodynamic bounds on spectral perturbations, with applications to oscillations and relaxation dynamics
• Large deviations for the Skew-Detailed-Balance Lifted-Markov processes to sample the equilibrium distribution of the Curie-Weiss model
• Irreversible Samplers from Jump and Continuous Markov Processes
• Freezing in stripe states for kinetic Ising models: a comparative study of three dynamics
• Irreversible Boltzmann samplers in dense liquids: weak-coupling approximation and mode-coupling theory
• Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics
• Random walks on rings and modules
• On decompositions of non-reversible processes
• Simulated tempering with irreversible Gibbs sampling techniques
• Microscopic and macroscopic perspectives on stationary nonequilibrium states