A Markov State Modeling analysis of sliding dynamics of a 2D model

摘要

Non-equilibrium Markov State Modeling (MSM) has recently been proposed [Phys.Rev. E 94, 053001 (2016)] as a possible route to construct a physical theory ofsliding friction from a long steady state atomistic simulation: the approachbuilds a small set of collective variables, which obey a transition-matrixbased equation of motion, faithfully describing the slow motions of the system.A crucial question is whether this approach can be extended from the original1D small size demo to larger and more realistic size systems, without aninordinate increase of the number and complexity of the collective variables.Here we present a direct application of the MSM scheme to the sliding of anisland made of over 1000 harmonically bound particles over a 2D periodicpotential. Based on a totally unprejudiced phase space metric and withoutrequiring any special doctoring, we find that here too the scheme allowsextracting a very small number of slow variables, necessary and sufficient todescribe the dynamics of island sliding.