On the Heat Death and the Big Crunch
In Memory of Jerry Ericksen
This article is an exercise in elementary mechanics and thermodynamics. It emphasizes the basic difference between mechanics and thermodynamics which lies in the irreversibility of the latter theory. Clausius  (Poggendorff’s Annalen der Physik, p. 125, 1865) – the discoverer of entropy – was led to express the dichotomy in the famous slogan die Energie der Welt ist constant, and die Entropie der Welt strebt einem Maximum zu. (Gibbs put these slogans on top of his comprehensive memoir  (Gibbs, On the Equilibrium of Heterogeneous Substances, pp. 108–248, 1876).) And again Clausius  (Über den zweiten Hauptsatz der mechanischen Wärmetheorie, A lecture given at the general session of German natural scientists and physicians in Frankfurt/M on September 23, 1867, 1867) invented the notion of the heat death as the final destiny of the world. Nowadays it has become quiet around the heat death. Says Asimov  (Asimov’s Biographical Encyclopedia of Science and Technology, 1975): “Though the laws of thermodynamics stand as firmly as ever, cosmologists ... [show] a certain willingness to suspend judgement on the matter of heat death.” And we, the authors of this article, might add that present-day cosmologists know so little about the universe that heat death is a tiny spot in the sea of ignorance and therefore not worthy of discussion by serious scientists. All the more reason to take a fresh look at the subject. Now, however, this article is most definitely not a contribution to formal and technical cosmology as described in the monograph  (Cosmology, 2008) by S. Weinberg, or the popular booklet  (Fundamentals. Ten Keys to Reality, 2021) by F. Wilczek. Far from it! We treat a monatomic ideal gas under adiabatic conditions in two situations: The gas in a cylinder under a locked piston which – at some instance – is released; and a homogeneous cloud of gas at rest when – at some time – gravitation is “switched on”. It is only by a big leap of imagination that the two cases may be viewed as models for the universe. We also admit that we do not know whether the universe is adiabatic and free of working. Clausius and Gibbs thought so and we follow authority and investigate the validity of the prediction of the heat death and the related idea of the big crunch under these assumptions. We shall confirm the heat death as a very hot event but refute the big crunch.
Published in: Journal of Elasticity, 10.1007/s10659-022-09926-z, Springer Nature