Entropy variation in a fractal phase space

Abstract

In this work, with the help of fractional calculus, it is shown a time dependence of entropy more general than the well known Pesin relation is derived. Here the equiprobability postulate is not assumed, the system dynamic in the phase space is not necessarily Markovian and the system is not in a steady state at all. Different possibilities for the time evolution of entropy by considering different features of the phase space and processes involved are obtained.