  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.
