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

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.

Heating, Cooling, and Equilibration of an Interacting Many-Fermion System

We discuss the process of equilibrium’s attainment in an interacting many-fermions system linked to a heat reservoir, whose temperature T is subject to a short-time disturbance of total duration 2τ. In this time-interval, its temperature increases up to a maximum value , cooling off afterward (also gradually) to its original value TM. The process is described by a typical master equation that leads eventually to equilibration. We discuss how the equilibration process depends upon 1) the system’s fermion-number, 2) the fermion-fermion interaction’s strength V, 3) the disturbance duration 2τ, and finally 4) the maximum number of equations N of the master equation.