Abstract
Main thermodynamic functions for an adiabatically isolated body with a constant internal energy have been determined within the formalism of covariant quantum theory with reparameterization invariance of intrinsic time. The modification does not change the dynamic content of the theory on the classical level; however, it makes it possible to determine the unitary evolution operator in the quantum theory. In this operator, intrinsic time is a measure of internal motion of a body. A transition to statistical mechanics is performed by Wick rotation of intrinsic time in a complex plane. As a result, representation of the partition function of an isolated body in the form of Euclidean functional integral over the space of closed trajectories in the configuration space is obtained. The average reciprocal temperature and free energy, which underlie the thermal mechanics of an adiabatically isolated body, are determined for a specified internal energy.
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REFERENCES
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1995; Pergamon, Oxford, 1980).
Ch. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996).
V. R. Regel’, A. I. Slutsker, and E. E. Tomashevskii, The Kinetic Nature of the Strength of Solids (Nauka, Moscow, 1974) [in Russian].
J. P. Joule, Proc. R. Soc. 8, 355 (1857).
W. Thompson (Lord Kelvin), Trans. R. Soc. Edinburgh 20, 261 (1853).
A. A. Benam, G. Viola, and T. Korakianitis, J. Therm. Anal. Calorim. 100, 941 (2010).
T. Dauxois and S. Ruffo, Scholarpedia 3, 5528 (2008).
M. A. Porter, N. J. Zabusky, B. Hu, and D. K. Campbell, Am. Sci. 97, 214 (2009).
M. Onorato, L. Vozella, D. Proment, and Y. V. Lvov, Proc. Nat. Acad. Sci. U. S. A. 112, 4208 (2015).
R. Anufriev, S. Gluchko, S. Volz, and M. Nomura, ACS Nano 12, 11928 (2018).
O. S. Loboda, E. A. Podolskaya, D. V. Tsvetkov, and A. M. Krivtsov, Continuum Mech. Thermodyn. (2020). https://doi.org/10.1007/s00161-020-00921-0
V. A. Kuzkin and A. M. Krivtsov, Phys. Rev. 101, 042209 (2020).
R. Feynmann and A. Hibbs, Quantum Mechanics and Path Integrals (Dover, New York, 2010).
J. Govaerts, CERN-TH No. 5010/88 (CERN, 1988).
R. P. Feynman, Statistical Mechanics (Benjamin, MA, 1972).
N. N. Gorobei and A. S. Luk’yanenko, Phys. Solid State 62, 2400 (2020).
H. C. Ottinger, A Philosophical Approach of Quantum Field Theory (Cambridge Univ. Press, Cambridge, 2018). https://doi.org/10.1017/9781108227667
M. E. Peskin and D. V. Schroeder, Introduction of Quantum Field Theory (CRC, Boca Raton, FL, 2019).
N. N. Gorobei and A. S. Luk’yanenko, Phys. Solid State 61, 650 (2019).
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Translated by A. Sin’kov
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Gorobei, N.N., Luk’yanenko, A.S. On the Thermodynamic Parameters of an Adiabatically Isolated Body. Phys. Solid State 63, 706–708 (2021). https://doi.org/10.1134/S1063783421050073
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DOI: https://doi.org/10.1134/S1063783421050073