Velocity Trapping in the Lifted Totally Asymmetric Simple Exclusion Process and the True Self-Avoiding Random Walk

We discuss nonreversible Markov-chain Monte Carlo algorithms that, for particle systems, rigorously sample the positional Boltzmann distribution and that have faster than physical dynamics. These algorithms all feature a nonthermal velocity distribution. They are exemplified by the lifted totally asymmetric simple exclusion process (lifted TASEP), a one-dimensional lattice reduction of event-chain Monte Carlo. We analyze its dynamics in terms of a velocity trapping that arises from correlations between the local density and the particle velocities. This allows us to formulate a conjecture for its out-of-equilibrium mixing timescale, and to rationalize its equilibrium superdiffusive timescale. Both scales are faster than for the (unlifted) TASEP. They are further justified by our analysis of the lifted TASEP in terms of many-particle realizations of true self-avoiding random walks. We discuss velocity trapping beyond the case of one-dimensional lattice models and in more than one physical dimensions. Possible applications beyond physics are pointed out.