Brief Review of Pertinent Concepts

Abstract

This chapter is meant to provide a neither complete nor irreducible overview of the ideas and arguments which have been brought forward during the search for a derivation of thermodynamics. A central issue in these efforts has been the irreversibility which is most likely absent in any underlying theory. Among others, we give a brief summary of central classical concepts such as the Boltzmann equation, H–Theorem, ergodicity, the ensemble as introduced by Gibbs and Ehrenfest’s view on the subject. Furthermore we discuss the Shannon entropy, the von Neumann entropy, and the theory of open quantum systems within the quantum mechanical regime. Any “decision ” in favor of any of those approaches is left to the reader. Here, only the most prominent ideas that are or have been around are briefly introduced.

Given the success of Ludwig Boltzmann’s statistical approach in explaining the observed irreversible behavior of macroscopic systems …, it is quite surprising that there is still so much confusion about the problem of irreversibility.

— J. L. Lebowitz [1]

Boltzmann’s ideas are as controversial today, as they were more than hundred years ago, yet they are still defended (Lebowitz 1993). Boltzmann’s H-Theorem is based on the unjustifiable assumption that the motions of particles are uncorrelated before collision.

— H. Primas [2]