Entropy, Probability and Dynamics

TL;DR

This paper traces the historical development of the concept of entropy from Boltzmann to modern dynamical systems, highlighting the evolving interpretations from probabilistic to dynamical foundations.

Contribution

It provides a comprehensive overview of the progression from classical to quantum and chaotic interpretations of entropy, emphasizing the dynamical basis of the Sinai-Ruelle-Bowen distribution.

Findings

Historical connections between entropy and probability are outlined.

Quantum modifications to classical entropy-probability relations are discussed.

The dynamical interpretation of entropy in chaotic systems is exemplified.

Abstract

Boltzmann's struggle with a derivation of the Second Law of Thermodynamics is sketched. So is his first derivation of the connection between entropy and probability in 1877. Planck's derivation and quantum mechanical modifications of Boltzmann's connection between entropy probability are given next. Then Einstein's objections to a purely probabilistic rather than a dynamical interpretation of entropy are discussed. Finally, the dynamical basis of the Sinai-Ruelle-Bowen distribution for very chaotic systems is sketched and appears to be an example of Einstein's dynamical interpretation of entropy.