Entropy variation in a fractal phase space

TL;DR

This paper derives a generalized time-dependent entropy relation in fractal phase spaces using fractional calculus, relaxing assumptions like equiprobability, Markovian dynamics, and steady state conditions.

Contribution

It introduces a novel approach to entropy evolution in complex systems without relying on traditional assumptions, broadening the understanding of non-Markovian and non-steady state dynamics.

Findings

Derived a generalized entropy time dependence using fractional calculus.

Showed entropy evolution without assuming equiprobability or steady state.

Explored various phase space features affecting entropy dynamics.

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.