A model of classical thermodynamics based on the partition theory of integers, Earth gravitation, and semiclassical asymptotics. I

Abstract

In the paper, a new construction of the theory of partitions of integers is proposed. The author defines entropy as the natural logarithm of the number of partitions of a number M into natural summands with repetitions allowed p(M) and repetitions forbidden q(M). The passage from ln p(M) to lnq(M) through the mesoscopic values M → 0 is studied. The topological transition from the mesoscopic lower levels of the Bohr–Kalckar construction to the macroscopic levels corresponding to the critical number of neutrons according to the consequence of Einstein’s inequality M ≤ c N c , where c is determined for the particles of the given atomic nucleus. The role of quantum mechanics in establishing the new world outlook in physics is analyzed. It is pointed out that the main equations of thermodynamics in the volume “Statistical Physics” of the Landau–Lifshits treatise are obtained without appealing to the so-called “three main principles of thermodynamics”. It is also pointed out that Niels Bohr’s liquid model of the nucleus does not involve any interaction of particles in the form of attraction and is based on the presence of a common potential trough for all elements of the nucleus. The author constructs a new approach to thermodynamics, using quantum mechanics and the Earth’s gravitational attraction as a common potential trough.