A Model of Classical Thermodynamics Based on the Partition Theory of Integers, Earth Gravitation, and Semiclassical Asymptotics. I

Russian Journal of Mathematical Physics. 2017. Vol. 24. No. 3. P. 354–372.

Maslov V. P.

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 <= cNc, 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.

Keywords: entropy, thermodynamics, theory of partitions of integers, topological transition, quantum mechanics, Earth’s gravitational attraction