On the Statistical Viewpoint Concerning the Second Law of Thermodynamics  A Reminder on the Ehrenfests' Urn Model
Abstract
In statistical thermodynamics the 2nd law is properly spelled out in terms of conditioned probabilities. As such it makes the statement that "entropy increases with time" without preferring a time direction. In this paper we wish to explain and illustrate this statement in terms of the Ehrenfests' urn model in a way that hopefully adds some clarifying aspects concerning the role of timeconditioned probabilities. We will relate past and futureconditioned probabilities through Bayes' rule, which allows us to explicitly state what is meant by timereversal invariance in this context.
 Publication:

From Quantum to Classical; Essays in Honour of H.Dieter Zeh
 Pub Date:
 2022
 DOI:
 10.1007/9783030887810_11
 arXiv:
 arXiv:physics/0509220
 Bibcode:
 2022fqce.book..225G
 Keywords:

 Physics  General Physics;
 82B30
 EPrint:
 18 pages, no figures. This paper is my contribution to the book "From Quantum to Classical  Essays in Honour of H.Dieter Zeh", edited by Claus Kiefer, that appeared in 2022 as volume 204 in the series Fundamental Theories of Physics at Springer Verlag. It is an extended version of the previous version (V1) containing an additional introduction and more references