Information-Based Numerical Distances between Equilibrium and Non-Equilibrium States

Abstract

We consider a typical master equation describing thermal time-evolution. In parallel, we also consider a quasi static canonical description of the same problem. We are able to devise a way of numerically comparing these two treatments and concoct a distance-measure between them. In this way, one is in a position to know how far or close equilibrium and off-equilibrium can get. The first, rather surprising observation, is that our systems lose structural details as N grows. Also, the time-evolution of the distance between the two pertinent probability distributions is quite sensitive to the heating-cooling process.