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We discuss a non-reversible Markov chain Monte Carlo (MCMC) algorithm for particle systems, in which the direction of motion evolves deterministically. This sequential direction-sweep MCMC generalizes the widely spread MCMC sweep methods for particle or spin indices. The sequential direction-sweep MCMC can be applied to a wide range of original reversible or non-reversible Markov chains, such as the Metropolis algorithm or the event-chain Monte Carlo algorithm. For a simplified two-dimensional dipole model, we show rigorously that sequential MCMC leaves the stationary probability distribution unchanged, yet it profoundly modifies the Markov-chain trajectory. Long excursions, with persistent rotation in one direction, alternate with long sequences of rapid zigzags resulting in persistent rotation in the opposite direction. We show that sequential MCMC can have shorter mixing times than the algorithms with random updates of directions. We point out possible applications of sequential MCMC in polymer physics and in molecular simulation.
The event-chain Monte Carlo (ECMC) method is an irreversible Markov process based on the factorized Metropolis filter and the concept of lifted Markov chains. Here, ECMC is applied to all-atom models of multi-particle interactions that include the lo
We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions
We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain dynamics leads
We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heatbath or Metropolis algorithms. The mixing time scales appear to fall into two distinct unive
An overarching action principle, the principle of minimal free action, exists for ergodic Markov chain dynamics. Using this principle and the Detailed Fluctuation Theorem, we construct a dynamic ensemble theory for non-equilibrium steady states (NESS