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

## TL;DR

This paper demonstrates that Markov State Modeling can effectively analyze the sliding dynamics of a large 2D particle island, identifying key slow variables without complex pre-processing, thus extending its applicability to more realistic systems.

## Contribution

The study applies MSM to a large 2D system, showing it can extract essential slow variables for sliding dynamics without needing specialized metrics or modifications.

## Key findings

- MSM successfully identifies few slow variables in a 2D sliding system.
- The approach works without specialized phase space metrics.
- It extends MSM applicability to larger, more realistic systems.

## 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.