Abstract
Fluctuations in open subsystems with a small number of particles and fixed volume immersed in an equilibrium system (thermostat) are treated. Within the framework of classical thermodynamics, the distribution functions of fluctuations of the number of particles, momentum, and energy in these subsystems are derived. These results are compared with the corresponding data obtained for hard spheres using the method of molecular dynamics. Their satisfactory agreement is observed. It is demonstrated that the distribution functions of fluctuations of the number of particles and energy are significantly different from both the Gauss and Poisson distribution. The distribution function of fluctuations of momentum of a small subsystem is Gaussian and independent of the density of the thermostat.
Similar content being viewed by others
REFERENCES
Rudoi, Yu.G. and Sukhanov, A.D., Usp. Fiz. Nauk, 2000, vol. 170, no. 12, p. 1265.
Rudyak, V.Ya., Kharlamov, G.V., and Belkin, A.A., Pis'ma Zh. Tekh. Fiz., 2000, vol. 26, no. 13, p. 29.
Rudyak, V.Ya., Kharlamov, G.V., and Belkin, A.A., Teplofiz. Vys. Temp., 2001, vol. 39, no. 2, p. 283 (High Temp. (Engl. transl.), vol. 39, no. 2, p. 264).
Einstein, A., Izbrannye sochineniya (Selected Works), Moscow: Nauka, 1966, vol. 3, p. 216.
Chandrasekhar, S., Stochastic Problems in Physics and Astronomy, New York: AIP, 1943. Translated under the title Stokhasticheskie problemy v fizike i astronomii, Moscow: Izd. Inostrannaya Literatura, 1947.
Landau, L.D. and Lifshits, E.M., Statisticheskaya fizika (Statistical Physics), Moscow: Nauka, 1976, Part 1.
Rumer, Yu.B. and Ryvkin, M.Sh., Termodinamika, statisticheskaya fizika i kinetika (Thermodynamics, Statistical Physics, and Kinetics), Moscow: Nauka, 1977.
Carnahan, H.F. and Starling, K.E., J. Chem. Phys., 1969, vol. 51, p. 635.
Rudyak, V.Ya. and Belkin, A.A., Zh. Eksp. Teor. Fiz., 1999, vol. 116, issue 5(11), p. 2006.
Norman, G.E. and Stegailov, V.V., Zh. Eksp. Teor. Fiz., 2001, vol. 119, issue 5, p. 1011.
Morozov, I.V., Norman, G.E., and Valuev, A.A., Phys. Rev. E, 2001, vol. 63, no. 3, p. 3405.
Alder, B.J. and Wainright, T.E., Phys. Rev. Lett., 1967, vol. 18, no. 23, p. 988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rudyak, V.Y., Kharlamov, G.V. The Theory of Equilibrium Fluctuations of Thermodynamic Quantities in Open Systems with a Small Number of Particles. High Temperature 41, 201–209 (2003). https://doi.org/10.1023/A:1023373517457
Issue Date:
DOI: https://doi.org/10.1023/A:1023373517457