Gleichverteilung --- Entropie. (Das Entropiespiel von T. und P. Ehrenfest) [oder: Über Hausfrauen und Dämone]. (Uniform distribution --- entropy. (The urn-model of T. and P. Ehrenfest) [or: on house-wives and demons]) (Q1803499)

The main purpose of this paper is to illustrate ideas of Boltzmann on statistical thermodynamics using the theory of uniform distribution. The work contains a lot of interesting historical remarks and several instructive models, e.g. motivated by Polya-Szegö a probabilistic model of Ehrenfest is replaced by a deterministic one (the change of a state is influenced by the behaviour of a sequence \((n\alpha)\) mod 1, \(\alpha\) an irrational number), demonstrating that the entropy in the sense of Boltzmann is increasing (with respect to classical statistics and Bose statistics) or describing types of Maxwell demons. It is demonstrated by elementary calculations that the demon's work requires not only energy but also entropy. Using results on the discrepancy of sequences also quantitative results are obtained (explicit bounds for the appearance of certain phenomena).