Abstract
A parallel between physical derivation and mathematical proof in classical thermodynamics is drawn. A relationship between thermodynamics and analytic number theory is demonstrated.
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V. P. Maslov, “Stationary-phase method for Feynman’s continual integral,” Teoret. Mat. Fiz. 2 (1), 30–35 (1970) [Theoret. and Math. Phys. 2 (1), 21–25 (1970)].
V. Guillemin and S. Sternerg, Geometric Asymptotics, (Amer. Math. Soc., Providence, RI, 1977).
V. P. Maslov, “What I learned from B. M. Levitan,” Math. Notes 96 (1–2), 3–9 (2014).
L. D. Landau and E. M. Lifshits, Statistical Physics (Nauka, Moscow, 1964) [in Russian].
V. P. Maslov, “New Approach to Classical Thermodynamics,” Math. Notes 100 (1–2), 154–185 (2016).
V. P. Maslov and V. E. Nazaikinskii, “Conjugate variables in analytic number theory. Phase space and Lagrangian manifolds,” Math. Notes 100 (3–4), 421–428 (2016).
A. G. Postnikov, Introduction to Analytic Number Theory (Nauka, Moscow, 1971) [in Russian].
B. M. Bredikhin, “Elementary solution of inverse problems on bases of free semigroups,” Mat. Sb. 50 (92) (2), 221–232 (1960).
V. P Maslov and V. E. Nazaikinskii, “Disinformation theory for bosonic computational media,” Math. Notes 99 (5–6), 895–900 (2016).
F. M. Donny, Acad. Bruxelles 17 (1843); see also Ann. Chim. (Phys.) 16 167 (1946).
A. T. Hayward, “Negative pressure in liquids: Can it be harnessed to serve man?” American Scientist 59, 434 (1971).
V. P. Maslov, “Analytic number theory and disinformation,” Mat. Zametki 100 (4), 553–565 (2016) [Math. Notes 100 (3–4), 568–578 (2016)].
R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, A Wiley-Interscience Publication (John Wiley and Sons, New York–London–Sydney–Toronto, 1975; Mir, Moscow, 1978), Vol. 1.
V. P. Maslov, “Mathematical aspects of weakly nonideal Bose and Fermi gases on a crystal base”, Funktsional. Anal. i Prilozhen. 37 (2), 16–27 (2003) [Functional Anal. Appl. 37 (2), 94–102 (2003)].
V. P Maslov, “Case of less than two degrees of freedom, negative pressure and the Fermi–Dirac distribution for a hard liquid,” Math. Notes 98 (1–2), 138–157 (2015).
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Maslov, V.P. Modern thermodynamics as a branch of mathematics (mathematical physics). Math Notes 100, 413–420 (2016). https://doi.org/10.1134/S0001434616090078
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DOI: https://doi.org/10.1134/S0001434616090078