Fast irreversible Markov chains in statistical mechanics

The Markov-chain Monte Carlo method is an outstanding computational tool in science. Since its origins, it has relied on the detailed-balance condition and the Metropolis algorithm to solve general computational problems under the condition of thermodynamic equilibrium with zero probability flows.
In this talk, I discuss a class of 'event-chain' algorithms that violate detailed balance yet satisfy global balance (the Markov chains are irreversible). Equilibrium is realized as a steady state with non-vanishing probability flows. The time-honored Metropolis acceptance criterion based on the change in the energy is replaced by a consensus rule originating in the new factorized Metropolis filter. The system energy is not computed, providing a fresh perspective for long-range interactions. Moves are infinitesimal and persistent, and they implement the lifting concept. The resulting general class of fast algorithms overcomes the limitation of detailed balance and also goes beyond hybrid Monte Carlo.
As applications I discuss our recent solution of the two-dimensional melting problem for hard disks and general potentials, and present the cell-veto algorithm for treating long-range systems without cutoffs nor Ewald summations. I will also discuss some open mathematical and algorithmic problems as well as connections of our algorithms with the totally asymmetric simple exclusion process (TASEP) and related processes.