A Markov state modeling analysis of sliding dynamics of a 2D model

Abstract

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 of sliding friction from a long steady state atomistic simulation: the approach builds a small set of collective variables, which obey a transition-matrix based equation of motion, faithfully describing the slow motions of the system. A crucial question is whether this approach can be extended from the original 1D small size demo to larger and more realistic size systems, without an inordinate increase of the number and complexity of the collective variables. Here we present a direct application of the MSM scheme to the sliding of an island made of over 1000 harmonically bound particles over a 2D periodic potential. Based on a totally unprejudiced phase space metric and without requiring any special doctoring, we find that here too the scheme allows extracting a very small number of slow variables, necessary and sufficient to describe the dynamics of island sliding.

Non-equilibrium Markov state modeling of periodically driven biomolecules

“…A key ingredient is the detailed balance condition linking forward and backward transition probabilities to energy changes, which drastically facilitates the construction of MSMs [6]. Recently, some efforts have been undertaken to extend MSMs towards driven systems such as modelling sliding friction [7,8], time-dependent external fields [9], and polymer collapse in shear flow [10].…”