Abstract
We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through the momentum current. We show that although the two expectation values converge to the same equilibrium value in the thermodynamic limit, the variance of the mechanical pressure is in general greater than that of the pressure defined through the thermodynamic relation. We also present a condition for experimentally detecting the difference between them in an idealized measurement of momentum transfer.
References
Einstein, A.: Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes. Ann. Phys. 33, 1275–1298 (1910)
Callen, C.H.: Thermodynamics and an Introduction to Thermostatistics, 2nd edn. Willey, New York (1985)
Landau, L.D., Lifshitz, E.M.: Statistical Physics, 3rd edn. Butterworth-Heinmann, Oxford (1980)
Mishin, Y.: Thermodynamic theory of equilibrium fluctuations. Ann. Phys. 363, 48–97 (2015)
Ernst, M.H., Hauge, E.H., Van Leeuwen, J.M.J.: Asymptotic time behavior of correlation functions. II. Kinetic and potential terms. J. Stat. Phys. 15, 7–22 (1976)
Kawasaki, K.: Mode Coupling and Critical Dynamics. In: Domb, C., Green, M.S. (eds.) Phase Transition and Critical Phenomena, vol. 5A, pp. 165–403. Academic Press, New York (1976)
Münster, A.: The theory of fluctuation. In: de Groot, S.R. (eds.) Proc. Enrico Fermi Intl. School of Physics, pp. 23–130. Varenna, Italy (1959)
Wallace, D.C.: Theory of stress fluctuations. Phys. Rev. E 62, 3077–3082 (2000)
Kittel, C.: Temperature fluctuation: an oxymoron. Phys. Today 41, 93 (1988)
Gibbs, J.W.: Elementary Principles in Statistical Mechanics. Scribner’s, New York (1902)
Presutti, E.: A mechanical definition of the thermodynamic pressure. J. Stat. Phys. 13, 301–314 (1975)
Itami, M., Sasa, S.: Derivation of Stokes’ Law from Kirkwood’s formula and the Green-Kubo formula via large deviation theory. J. Stat. Phys. 161, 532–552 (2015)
Acknowledgements
The authors thank Yoshi Oono for his useful comments. The present work was supported by KAKENHI Nos. 25103002 and 17H01148.
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Hiura, K., Sasa, Si. How Does Pressure Fluctuate in Equilibrium?. J Stat Phys 173, 285–294 (2018). https://doi.org/10.1007/s10955-018-2134-6
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DOI: https://doi.org/10.1007/s10955-018-2134-6