Abstract
We construct a natural measure on the thermodynamic Lagrangian manifold. The measure is defined via the kinetic coefficients. We study the accuracy of the asymptotics provided by the canonical operator for the derivatives of the logarithm of the partition function.
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L. D. Landau and E. M. Lifshits, Course of Theoretical Physics. Vol. 5: Statistical Physics [in Russian], GITTL, Moscow, 1951; English transl.: Pergamon Press, Oxford, 1968.
R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965.
V. P. Maslov, Perturbation Theory and Asymptotic Methods [in Russian], Izdat. Moskov. Univ., Moscow, 1965; French transl.: Dunod, Paris, 1972.
V. P. Maslov, Asymptotic Methods and Perturbation Theory [in Russian], Nauka, Moscow, 1988.
V. I. Arnold, Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow, 1989; English transl.: Springer-Verlag, New York, 1989.
V. P. Maslov, “Analytic extension of asymptotic formulas, and the axiomatics of thermodynamics and quasithermodynamics,” Funkts. Anal. Prilozhen., 28:4 (1994), 28–41; English transl.: Funct. Anal. Appl., 28:4 (1994), 247–256.
V. P. Maslov, “Geometric quantization of thermodynamics, phase transitions and asymptotics at critical points,” Mat. Zametki, 56:3 (1994), 155–156; English transl.: Math. Notes, 56:3–4 (1994), 984–985.
R. P. Feynman, Statistical Mechanics, Benjamin, Reading, 1972.
S. R. de Groot, Thermodynamics of Irreversible Processes, North-Holland, Amsterdam, 1952.
R. Kubo, Thermodynamics, North-Holland, Amsterdam, 1968.
A. Münster, Chemische Thermodynamik, Akademie-Verlag, Berlin, 1969.
V. P. Maslov, “The “lack of preference” law and the corresponding distributions in frequency probability theory,” Mat. Zametki, 80:2 (2006), 220–230.
V. P. Maslov, “The Zipf-Mandelbrot law: quantization and an application to the stock market,” Russ. J. Math. Phys., 12:4 (2005), 483–488.
V. P. Maslov, “Quantum linguo-statistics,” Russ. J. Math. Phys., 2006 (to appear).
V. P. Maslov, “On a general theorem of set theory resulting in the Gibbs, Bose-Einstein, and Pareto distributions and in the Zipf-Mandelbrot law for stock market,” Mat. Zametki, 78:6 (2005), 870–877.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 40, No. 3, pp. 12–29, 2006
Original Russian Text Copyright © by V. P. Maslov and V. E. Nazaikinskii
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Maslov, V.P., Nazaikinskii, V.E. Tunnel canonical operator in thermodynamics. Funct Anal Its Appl 40, 173–187 (2006). https://doi.org/10.1007/s10688-006-0029-9
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DOI: https://doi.org/10.1007/s10688-006-0029-9