Abstract
The maximum entropy formalism is used to investigate the growth of entropy (H-theorem) for an isolated system of hard spheres in an external potential under general boundary geometry. Assuming that only correlations of a finite number of particles are controlled and the rest maximizes entropy, we obtain an H-theorem for such a system The limiting cases such as the modified Enskog equation and linear kinetic theory are discussed.
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REFERENCES
J. W. Gibbs, Elementary Principles in Statistical Mechanics (Dover, New York, 1960).
A. I. Khinchin, Mathematical Foundations of Information Theory (Dover, New York, 1957).
J. L. Lebowitz, Boltzmann's entropy and time's arrow, Phys. Today 46:36–38 (1993).
J. L. Lebowitz, Microscopic reversibility and macroscopic behavior: Physical explanations and mathematical derivations, in 25 Years of Non-Equilibrium Statistical Mechanics, Proceedings, Sitges Conference, Barcelona, Spain, 1994, in Lecture Notes in Physics, J. J. Brey, J. Marro, J. M. Rubí, and M. San Miguel, eds. (Springer, 1995).
L. Boltzmann, Lectures on Gas Theory (Dover, New York, 1995).
J. Karkheck and G. Stell, Maximization of entropy, kinetic equations and irreversible thermodynamics, Phys. Rev. A 25:3302–3334 (1982).
J. Karkheck, H. van Beijeren, I. de Schepper, and G. Stell, Kinetic theory and H theorem for a dense square well fluid, Phys. Rev. A 32:2517–2520 (1965).
J. Bławzdziewicz and G. Stell, Local H-theorem for a Kinetic Variational Theory, J. Stat. Phys. 56:821–840 (1989).
L. Romero-Salazar, M. Mayorga, and R. M. Velasco, Maximum entropy formalism for a dense gas, Physica A 237:150–168 (1997).
H. van Beijeren, Kinetic theory of dense gases and liquids, Fundamental Problems in Statistical Mechanics, Vol. VII, H. van Beijeren, ed. (North-Holland, Amsterdam, 1990).
C. Cercignani, V. I. Gerasimenko, and D. Ya. Petrina, Many-Particle Dynamics and Kinetic Equations (Kluwer, Dordrecht, 1997).
P. Resibois, H-theorem for the (modified) Enskog equation, J. Stat. Phys. 19:593–609 (1978).
J. Bławzdziewicz, B. Cichocki, and H. van Beijeren, H-theorem for a linear kinetic theory, J. Stat. Phys. 66:607–633 (1992).
R. Evans, The nature of the liquid-vapour interface and other topics in the statistical mechanics of nonuniform classical fluids, Adv. Phys. 28:143–200 (1979).
A. Planes and E. Vives, Entropic formulation of statistical mechanics, J. Stat. Phys. 106:827–850 (2002).
D. Ruelle, Statistical Physics. Rigorous Results (Benjamin, New York Amsterdam, 1969).
J. Bławzdziewicz and B. Cichocki, Linear kinetic theory of hard sphere fluid, Physica A 127:38–71 (1984).
B. Cichocki, Enskog renormalization in linear kinetic theory, Physica A 142:245–272 (1987).
T. Morita and K. Hiroike, A new approach to the theory of classical fluids, Prog. Theor. Phys. 25:537–578 (1961).
R. J. Baxter, Three-particle hyper-netted chain approximation, Ann. Phys. (N.Y.) 46:509–545 (1968).
A. Bednorz, Graphical representation of the excess entropy, Physica A 298:400–418 (2001).
M. H. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. van Leeuwen, Physica 45:127 (1969).
H. van Beijeren, Ph.D. thesis, University Nijmegen (1974).
H. van Beijeren and M. H. Enrst, J. Stat. Phys. 12:125 (1979).
J. Piasecki, Kinetic theory of dense gases, Fundamental Problems in Statistical Mechanics, Vol. IV, E. G. D. Cohen and W. Fiszdon, eds. (Ossolineum, Wrocław, 1978).
H. van Beijeren, Equilibrium distribution of hard-sphere systems and revised Enskog theory, Phys. Rev. Lett. 51:1503–5 (1983).
M. Mareschal, J. Bławzdziewicz, and J. Piasecki, Local entropy production from the revised Enskog equation, Phys. Rev. Lett. 52:1169–1172 (1984).
J. Piasecki, Local H-theorem for the revised Enskog equation, J. Stat. Phys. 48:1203–1211 (1987).
G. E. Uhlenbeck and G. W. Ford, in Studies in Statistical Mechanics I, G. E. Uhlenbeck and J. de Boer, eds. (North-Holland, Amsterdam, 1962).
G. Stell, Cluster expansions for classical systems in equilibrium, in The Equilibrium Theory of Classical Fluids, H. Frish and J. Lebowitz, eds. (Benjamin, New York, 1964).
J. Percus, Theory of fluids, in The Equilibrium Theory of Classical Fluids, H. Frish and J. Lebowitz, eds. (Benjamin, New York, 1964).
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Bednorz, A., Cichocki, B. General H-Theorem for Hard Spheres. Journal of Statistical Physics 114, 327–360 (2004). https://doi.org/10.1023/B:JOSS.0000003114.38280.e4
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DOI: https://doi.org/10.1023/B:JOSS.0000003114.38280.e4