Normal solutions for master-equations with time-dependent transition rates - application to heating processes

Abstract

The long-time limit of the solutions of a master equation with time-dependent transition rates is analyzed, and the existence of a special (normal) solution, that all the other solutions tend to approach, is shown under quite general conditions. In general, the normal solution will be quite different from the time-dependent equilibrium distribution, although for not too fast continuous heating processes, it asymptotically tends to the equilibrium curve. The results seem to be relevant for the explanation of what is observed in real experiments. The general theory is applied to a very simple model, for which the normal solution is exactly found.