The entropy production paradox for fractional master equations

Abstract

Time-fractional evolution equations for probability distributions provide a means to describe an important class of stochastic processes. Their solutions show features, which are essential in modeling a variety of phenomena in real world applications. One aspect, which has been observed in time-fractional diffusion equations, shows a surprising and unexpected behavior of the entropy production rate induced by these equations. The entropy production rate increases as one moves away from the fully irreversible case, corresponding to classical diffusion. This rate is analyzed for a new class of systems with state spaces that are finite and denumerable. We find that the entropy production paradox reemerges nonetheless, but in a new and unexpected form.