Abstract
As is well known in statistical physics, the stationary distribution can be obtained by maximizing entropy. We show how one can reconstruct the formula for entropy knowing the formula for the stationary distribution. A general case is discussed and some concrete physical examples are considered.
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References
R. Balescu,Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, 1975).
D. Bernardin, Global invariants and equilibrium states in lattice gases,J. Stat. Phys. 68(3/4) (1992).
H. Cabannes, Global solution of the discrete Boltzmann equation with multiple collisions,Eur. J. Mech. B/Fluids 1992(4):415.
K. M. Case and P. Zweifel,Linear Transport Theory (Addison-Wesley, 1967).
S. K. Godunov and U. M. Sultangazin, On discrete models of the kinetic Boltzmann equation,Russ. Math. Surv. 26(3):1–6 (1971).
H. P. MacKean, Entropy is the only increasing functional of Kac's gas,Z. Wahrsch. 2:167 (1963).
Y. H. Qian, D. d'Humières, and P. Lallemand, Diffusion simulation with a deterministic one-dimensional lattice gas model,J. Stat. Phys. 68(3/4) (1992).
V. Vedenyapin, Differential forms in spaces without a norm. A theorem on the uniqueness of Boltzmann'sH-function,Russ. Math. Surv. 43(1):193 (1988).
L. Waldmann, Transporterscheinungen in Gasen von mittlerem Druck, inHandbuch der Physik, Vol. 12 (Springer, Berlin, 1958), p. 295.
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Arkhipov, Y., Klar, A. & Vedenyapin, V. On the connection of the formulas for entropy and stationary distribution. J Stat Phys 77, 1027–1037 (1994). https://doi.org/10.1007/BF02183149
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DOI: https://doi.org/10.1007/BF02183149