Geodesic
$H$ theorem for a homogeneous gas when allowance is made for various approximations in the density parameter
Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 3, pp. 402-413 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the truncated “free energy” $\Gamma[l]$ is extremal as a function of $g_1,g_2,\dots,g_l$ at the equilibrium point. This result is used in the framework of BBGKY theory to verify the necessary condition of nondecrease of the truncated free energy per unit volume. In addition, it is shown that such extremality is a “almost sufficient” condition for the validity of the $H$ theorem, namely, the “rate of change” of the truncated free energy differs from a nonnegative expression by terms of order $\varepsilon_0^{l+1}$ and higher, where $\varepsilon_0$ is the density parameter, provided surface effects are ignored. 
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     title = {$H$~theorem for a~homogeneous gas when allowance is made for various approximations in the density parameter},
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}
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R. L. Stratonovich. $H$ theorem for a homogeneous gas when allowance is made for various approximations in the density parameter. Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 3, pp. 402-413. http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a13/

[1] Boltsman L., Lektsii po kineticheskoi teorii gazov, GITTL, M., 1956

[2] Girshfelder Dzh., Kertis Ch., Berd R., Molekulyarnaya teoriya gazov i zhidkostei, IL, M., 1960

[3] Bogolyubov N. N., Problemy dinamicheskoi teorii v statisticheskoi fizike, GITTL, M.–L., 1946 | MR

[4] Cho S., Ulenbek Dzh., V knige: Ulenbek Dzh., Ford Dzh., Lektsii po statisticheskoi mekhanike, Mir, M., 1965

[5] Green M. S., “Boltzmann Equation from the statistical mechanical point of view”, J. Chem. Phys., 25:5 (1956), 836–855 | DOI | MR

[6] Cohen E. G. D., “On the generalization of the Boltzmann equation to general order in the density”, Physica, 28:10 (1962), 183–189 | DOI | MR

[7] Dorfman J. R., Cohen E. G. D., “Difficulties in the kinetic theory of dense gases”, J. Math. Phys., 8:2 (1967), 282–297 | DOI

[8] Sengers J. V., “Divergence in the density expantion of the transport coefficients of a two-dimensional gas”, Phys. Fluids, 9:9 (1966), 1685–1696 | DOI

[9] Prigozhin I., Neravnovesnaya statisticheskaya mekhanika, Mir, M., 1966

[10] Akhiezer A. I., Peletminskii S. V., Metody statisticheskoi fiziki, Nauka, M., 1977 | MR

[11] Klimontovich Yu. L., Kineticheskaya teoriya neidealnogo gaza i neidealnoi plazmy, Nauka, M., 1975 | MR

[12] Ursell H. D., Proc. Camb. Phyl. Soc., 23 (1927), 685 | DOI | Zbl

[13] Uhlenbeck G. E., Kahn B., Physica, 5 (1938), 399 | DOI

[14] de Boer J., Michels A., Physica, 6 (1939), 97 | DOI | Zbl

[15] Stratonovich R. L., Teoriya informatsii, Sov. Radio, M., 1975

[16] Kuznetsov P. I., Stratonovich R. L., “K matematicheskoi teorii korrelirovannykh sluchainykh tochek”, Izv. AN SSSR, ser. matem., 20:2 (1956), 167–178 | Zbl

[17] Stratonovich R. L., “Entropiya sistem so sluchainym chislom chastits”, ZhETF, 28:4 (1955), 409–421 | Zbl