The main characteristics of motion of an equilibrium system of potentially interacting material points in a nonuniform field of forces and the criteria determining the transition from discrete to thermodynamic system description are studied. A change in the internal energy of the system passing through a potential barrier is studied depending on the barrier width, the number of the system elements, and the initial conditions. It is demonstrated how the amplitude of fluctuations of the system energy parameters changes depending on the number of the material points. The D-entropy is evaluated. Two critical numbers are established. The first determines the number of the material points required for system transition to irreversible dynamics, and the second determines transition to the thermodynamic description. The conformity between the results obtained and the theoretical principles of system dynamics is analyzed.
Similar content being viewed by others
References
V. L. Ginzburg, Usp. Fiz. Nauk, 177, No. 4, 345–346 (2007).
I. Prigozhin, From Existing to Arising [in Russian], Nauka, Moscow (1980).
S. D. Haitun, Mechanics and Irreversibility [in Russian], Yanus Publishing House, Moscow (1996).
J. L. Lebowitz, Phys. Today, 46, 32–38 (1999).
G. M. Zaslavskii, Stochastics of Dynamic Systems [in Russian], Nauka, Moscow (1984).
M. Smolukhovskii, Usp. Fiz. Nauk, 93, No. 4, 724–737 (1967).
E. G. Cohen, NATO Sci. Series E: Appl. Sci., 371, 223 (1998).
V. V. Kadomtsev, Usp. Fiz. Nauk, 165, No. 8, 895–973 (1995).
B. G. Sidharth, Modelling Time, arXiv:0809.0587v1 [physics.gen-ph] (3 September, 2008).
N. Bor, Usp. Fiz. Nauk, LXVI, No. 4, 571–598 (1958).
Ya. G. Sinai, Modern Problems of Ergodic Theory [in Russian], Fizmatgiz, Moscow (1995).
G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford (1976).
V. M. Somsikov, M. A. Merzlyakov, and E. A. Malkov, Probl. Evol. Otkr. Sist., No. 1, 52–62 (1999).
V. M. Somsikov, Int. J. Bifurk. Chaos, 14, Nо. 11, 4027–4033 (2004).
V. M. Somsikov, J. Phys.: Conf. Series, 23, 7–16 (2005).
V. M. Somsikov, New Adv. Phys., 2, No. 2, 125–140 (2008).
V. M. Somsikov, Open Access Library J., 1–8 (2014).
V. M. Somsikov, From Newton’s Mechanics to Evolution Physics [in Russian], Nauka, Alma-Ata (2014).
L. D. Landau and E. M. Lifshits, Statistical Physics [in Russian], Nauka, Moscow (1976).
Yu. B. Rumer and M. Sh. Ryvkin, Thermodynamics, Statistical Physics, and Kinematics [in Russian], Nauka, Moscow (1977).
G. Goldstein, Classical Mechanics [in Russian], Nauka, Moscow (1975).
V. M. Somsikov and M. I. Denisenya, Russ. Phys. J., 56, No. 4, 463–472 (2013).
S. D. Khaitun, Vopr. Filos., No. 2, 62–74 (2013).
Yu. L. Klimontovich, Statistical Theory of Open Systems [in Russian], Yanus Publishing House (1995).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 30–39, November, 2015.
Rights and permissions
About this article
Cite this article
Somsikov, V.M., Andreev, A.B. On Criteria of Transition to a Thermodynamic Description of System Dynamics. Russ Phys J 58, 1515–1526 (2016). https://doi.org/10.1007/s11182-016-0677-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11182-016-0677-z