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A model of classical thermodynamics and mesoscopic physics based on the notion of hidden parameter, Earth gravitation, and quasiclassical asymptotics. II. (English) Zbl 1387.82026
Summary: This paper presents a new approach to thermodynamics based on two “first principles”: the theory of partitions of integers and Earth gravitation. The self-correlated equation obtained by the author from Gentile statistics is used to describe the effect of accumulation of energy at the moment of passage from the boson branch of the partition to its fermion branch. The branch point in the passage from bosons to fermions is interpreted as an analog of a jump of the spin. A hidden parameter – the measurement time as time of the Gödel numbering – is introduced.
For Part I see [the author, ibid. 24, No. 3, 354–372 (2017; Zbl 1394.82007)].

MSC:
82B30 Statistical thermodynamics
81V17 Gravitational interaction in quantum theory
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
80A10 Classical and relativistic thermodynamics
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[1] Maslov, V. P., A model of classical thermodynamics based on the partition theory of integers, Earth garvitation, and quasiclassical assymptotics. I, Russ. J. Math. Phys., 24, 354-372, (2017) · Zbl 1394.82007
[2] B. B. Kadomtsev, Collective Phenomena in Plasma (Nauka, Moscow, 1988) [in Russian].
[3] L. D. Landau and E. M. Lifshits, Statistical Physics (Nauka, Moscow, 1964) [in Russian]. · Zbl 0659.76001
[4] L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non- Relativistic Theory, 2nd ed. (Nauka, Moscow, 1964; translation of the 1st ed., Pergamon Press, London-Paris and Addison-Wesley Publishing Co., Inc., Reading, Mass., 1958).
[5] Maslov, V. P., On the hidden parameter in measurement theory, (2017) · Zbl 1383.81099
[6] Maslov, V. P., Two first principles of Earth surface thermodynamics. mesoscopy, energy accumulation, and the branch point in boson-fermion transition, (2017) · Zbl 1387.82027
[7] Bohr, N.; Kalckar, F., On the transformation of atomic nuclei due to collisions with material particles, Uspehhi Fiz. Nauk, 20, 317-340, (1938)
[8] Hardy, G. H.; Ramanujan, S., Asymptotic formulae in combinatorial analysis, Proc. London Math. Soc. (2), 17, 75-115, (1917) · JFM 46.0198.04
[9] Maslov, V. P., The Bohr-kalckar correspondence principle and a new construction of partitions in number theory, Math. Notes, 102, 533-540, (2017) · Zbl 1382.82015
[10] Maslov, V. P., New insight into the partition theory of integers related to problems of thermodynamics and mesoscopic physics, Math. Notes, 102, 234-251, (2017) · Zbl 1382.82017
[11] V. P. Maslov, Threshold Levels in Economics (arXiv:0903.4783v2 [q-fin.ST], 3 Apr 2009). · Zbl 1179.91214
[12] A. G. Postnikov, Introduction to Analytic Number Theory (Nauka, Moscow, 1971). · Zbl 0231.10001
[13] Maslov, V. P.; Nazaikinskii, V. E., Conjugate variables in analytic number theory. phase space and Lagrangian manifolds, Math. Notes, 100, 421-428, (2016) · Zbl 1357.82068
[14] Maslov, V. P.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E., Volume and entropy in abstract analytic number theory and thermodynamics, Math. Notes, 100, 828-834, (2016) · Zbl 1362.82025
[15] Dai, W.-S.; Xie, M., Gentile statistics with a large maximum occupation number, Ann. Physics, 309, 295-305, (2004) · Zbl 1037.81104
[16] Maslov, V. P., Topological phase transitions in the theory of partitions of integers, Russian J. Math. Phys., 24, 249-260, (2017) · Zbl 1457.82122
[17] Maslov, V. P., Bounds of the repeated limit for the Bose-Einstein distribution and the construction of partition theory of integers, Math. Notes, 102, 583-586, (2017) · Zbl 1382.82018
[18] Quack, J., Gravitation Casimir effect, Phys. Rev. Lett., 144, 081104, (2015)
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