Abstract
The local densities and current densities of conserved quantities are expressed in a tutorial scope, for a fluid under arbitrary off-equilibrium conditions, in terms of the two-particle potential W(r) and of the one- and two-particle densities in phase space f and f 2. When f and f 2 vary significantly over the range of W(r), the density and current density of energy are not defined in a unique fashion, so that conservation of energy can be implemented locally in many different ways. Owing to Galilean invariance, the stress tensor and the heat flux are defined even far from the hydrodynamic regime.
This article is supplemented with comments by Y. Pomeau and J. Piasecki.
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References
J. Yvon, La théorie statistique des fluides et l’équation d’état, Actual. Sci. et Indust. No. 203 (Hermann, Paris, 1935)
D. Massignon, Mécanique statistique des fluides; fluctuations et propriétés locales (Dunod, Paris, 1957)
G.E. Uhlenbeck, G.W. Ford, Lectures on statistical mechanics (Amer. Math. Soc., Providence, 1963)
P. Résibois, M. De Leener, Classical theory of fluids (Wiley, New York, 1977)
R. Balian, From microphysics to macrophysics, Vol. II, Chap. 14 (Springer, 2007)
References
G.E. Uhlenbeck, G.W.G. Ford, Amer. Math. Soc., Providence R.I. (1963)
P. Résibois, M. De Leener, Classical Kinetic Theory of Fluids (Wiley, New York, 1977)
D. Massignon, Mécanique Statistique des Fluides: Fluctuations et Propriétés Locales (Dunod, Paris, 1957)
J.G. Kirkwood, F.P. Buff, J. Chem. Phys. 17, 338 (1948)
J. Yvon, Le problème de la condensation, de la tension et du point critique, Colloque de thermodynamique, Proceedings edited by I. Prigogine (Brussels, IUPAP, 1949), p. 9
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Balian, R. Microscopic local conservation laws for classical fluids. Eur. Phys. J. Spec. Top. 224, 927–934 (2015). https://doi.org/10.1140/epjst/e2015-02436-5
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DOI: https://doi.org/10.1140/epjst/e2015-02436-5