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. © 2009 Springer-Verlag Berlin Heidelberg.