Generalized kinetic equations for dense gases and liquids in the Zubarev nonequilibrium statistical operator method and Renyi statistics

P. P. Kostrobii; A. V. Viznovych; B. B. Markiv; M. V. Tokarchuk

Generalized kinetic equations for dense gases and liquids in the Zubarev nonequilibrium statistical operator method and Renyi statistics

P. P. Kostrobii ; A. V. Viznovych ; B. B. Markiv ; M. V. Tokarchuk

Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 145-159 Cet article a éte moissonné depuis la source Math-Net.Ru

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Résumé

To describe kinetic processes in gases and liquids far from equilibrium, we obtain the nonequilibrium statistical operator (NSO) and the generalized kinetic equations for the nonequilibrium one- and two-particle distribution functions based on the Zubarev NSO method and the maximum entropy principle for the Renyi entropy. We consider a $q$-generalization of the Liouville equation and obtain its general solution using the NSO method.

Keywords: Renyi entropy, nonequilibrium statistical operator, generalized kinetic equation.

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     title = {Generalized kinetic equations for dense gases and liquids in {the~Zubarev} nonequilibrium statistical operator method and {Renyi} statistics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {184},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a9/}
}

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P. P. Kostrobii; A. V. Viznovych; B. B. Markiv; M. V. Tokarchuk. Generalized kinetic equations for dense gases and liquids in the Zubarev nonequilibrium statistical operator method and Renyi statistics. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 145-159. http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a9/

Bibliographie
Cité par

[1] K. Yoshida, T. Arimitsu, J. Phys. A: Math. Theor., 46:33 (2013), 335501, 15 pp. | DOI | MR | Zbl

[2] P. C. Valente, J. C. Vassilicos, The non-equilibrium region of grid-generated decaying turbulence, arXiv: 1307.5898

[3] M. Tokuyama, Phys. A, 395 (2014), 31–47, arXiv: 1409.4839 | DOI | MR

[4] P. Mendoza-Méndez, L. López-Flores, A. Vizcarra-Redón, L. F. Sánchez-Diaz, M. Medina-Noyola, Phys. A, 394 (2014), 1–16 | DOI | MR

[5] J. Du, Phys. A, 391:4 (2012), 1718–1728 | DOI

[6] R. Guo, J. Du, Phys. A, 406 (2014), 281–286 | DOI | MR

[7] J. P. Boon, J. F. Lutsko, C. Lutsko, Phys. Rev. E, 85:2 (2012), 021126, 7 pp., arXiv: 1110.5463 | DOI

[8] G. F. Mazenko, Phys. Rev. E, 81:6 (2010), 061102, 18 pp., arXiv: 0905.4904 | DOI | MR

[9] G. F. Mazenko, Phys. Rev. E, 83:4 (2011), 041125, 21 pp., arXiv: 1009.3008 | DOI

[10] S. P. Das, G. F. Mazenko, J. Statist. Phys., 152:1 (2013), 159–194, arXiv: 1303.1627 | DOI | MR | Zbl

[11] P. Kostrobij, R. Tokarchuk, M. Tokarchuk, B. Markiv, Condens. Matter Phys., 17:3 (2014), 33005, 9 pp. | DOI

[12] P. A. Hlushak, M. V. Tokarchuk, Condens. Matter Phys., 17:2 (2014), 23606, 14 pp. | DOI

[13] C. A. B. Silva, A. R. Vasconcellos, J. G. Ramos, R. Luzzi, J. Statist. Phys., 143:5 (2011), 1020–1034 | DOI | MR | Zbl

[14] C. A. B. Silva, J. G. Ramos, A. R. Vasconcellos, R. Luzzi, Nonlinear higher-order hydrodynamics. Unification of kinetic and hydrodynamic approaches within a nonequilibrium statistical ensemble formalism, arXiv: 1210.7280

[15] V. N. Tsytovich, U. de Andelis, Phys. Plasmas, 11:2 (2004), 496–506 | DOI | MR

[16] A. I. Olemskoi, Theory of Structure Transformations in Non-equilibrium Condensed Matter, Horizons in World Physics Series, 231, NOVA Science Publ., New York, 1999

[17] T. D. Frank, Nonlinear Fokker–Planck Equations. Fundamentals and Applications, Springer, Berlin, 2005 | MR | Zbl

[18] B. B. Markiv, R. M. Tokarchuk, P. P. Kostrobij, M. V. Tokarchuk, Phys. A, 390:5 (2011), 785–791 | DOI | MR

[19] J. P. Boon, S. Yip, Molecular Hydrodynamics, McGraw-Hill, New York, 1980 | MR

[20] I. Mryglod, M. Tokarchuk, Voprosy atomnoi nauki i tekhniki, 3:24 (1992), 134–139

[21] I. M. Mryglod, I. P. Omelyan, M. V. Tokarchuk, Mol. Phys., 84:2 (1995), 235–259 | DOI

[22] B. B. Markiv, I. P. Omelyan, M. V. Tokarchuk, Phys. Rev. E, 82:4 (2010), 041202, 11 pp. | DOI

[23] D. N. Zubarev, V. G. Morozov, I. P. Omelyan, M. V. Tokarchuk, TMF, 96:3 (1993), 325–350 | DOI | MR | Zbl

[24] M. V. Tokarchuk, I. P. Omelyan, A. E. Kobryn, Condens. Matter Phys., 1:4(16) (1998), 687–751 | DOI

[25] A. E. Kobryn, I. P. Omelyan, M. V. Tokarchuk, J. Statist. Phys., 92:5–6 (1998), 973–994 | DOI | MR | Zbl

[26] B. Markiv, I. Omelyan, M. V. Tokarchuk, J. Statist. Phys., 155:5 (2014), 843–866, arXiv: 1308.3627 | DOI | MR | Zbl

[27] B. Markiv, M. Tokarchuk, Phys. Plasmas, 21:2 (2014), 023707, 16 pp., arXiv: 1309.2509 | DOI

[28] D. N. Zubarev, Neravnovesnaya statisticheskaya termodinamika, Nauka, M., 1971 | MR

[29] C. Cercignani, V. I. Gerasimenko, D. Ya. Petryna, Many-Particle Dynamics and Kinetic Equations, Kluwer, Dordrecht, 1997 | MR | Zbl

[30] D. N. Zubarev, V. G. Morozov, G. Repke, Statisticheskaya mekhanika neravnovesnykh protsessov, v. 1, Fizmatlit, M., 2002 | MR | Zbl

[31] D. N. Zubarev, V. G. Morozov, G. Repke, Statisticheskaya mekhanika neravnovesnykh protsessov, v. 2, Fizmatlit, M., 2002 | MR | Zbl

[32] P. P. Kostrobij, M. V. Tokarchuk, B. M. Markovych, V. V. Ignatyuk, B. V. Gnativ, Reaction-diffusion Processes in the “Metal-Gas” Systems, Publishing House of Lviv Polytechnic National University, Lviv, 2009 , (in Ukrainian)

[33] C. Tsallis, J. Statist. Phys., 52:1–2 (1988), 479–487 | DOI | MR | Zbl

[34] A. Rényi, Probability Theory, Applied Mathematics and Mechanics, 10, North-Holland, Amsterdam, 1970 | MR | Zbl

[35] P. Turán (ed.), Selected Papers of Alfréd Rényi, v. 2, 1956–1961, Akadémiai Kiadó, Budapest, 1976 | MR

[36] B. D. Sharma, D. P. Mittal, J. Math. Sci., 10 (1975), 28–40 | MR

[37] E. Akturk, G. B. Bagci, R. Sever, Is Sharma-Mittal entropy really a step beyond Tsallis and Renyi entropies? , arXiv: cond-mat/0703277

[38] C. Beck, Contin. Mech. Thermodyn., 16:3 (2004), 293–304, arXiv: cond-mat/0303288 | DOI | MR | Zbl

[39] C. Beck, “Superstatistics: Theoretical concepts and physical applications”, Anomalous Transport: Foundations and Applications, eds. R. Klages, G. Radons, I. M. Sokolov, Wiley-VCH, New York, 2008, 433–457 | DOI

[40] S. Abe, Y. Okamoto (eds.), Nonextensive Statistical Mechanics and Its Applications, Lecture Notes in Physics, 560, Springer, Heidelberg, 2001 | DOI | MR | Zbl

[41] M. Gell-Mann, C. Tsallis (eds.), Nonextensive Entropy – Interdisciplinary Applications, Oxford Univ. Press, New York, 2004 | MR | Zbl

[42] C. Tsallis (ed.), Introduction to Nonextensive Statistical Mechanics. Approaching a Complex World, Springer, New York, 2009 | MR | Zbl

[43] C. Essex, C. Schulzky, A. Franz, K. H. Hoffmann, Phys. A, 284:1–4 (2000), 299–308 | DOI | MR

[44] J. P. Boon, J. F. Lutsko, Phys. A, 368:1 (2006), 55–62, arXiv: cond-mat/0508231 | DOI | MR

[45] T. Arimitsu, N. Arimitsu, Phys. Rev. E, 61:3 (2000), 3237–3240 | DOI

[46] F. M. Ramos, R. R. Rosa, C. R. Neto, M. J. A. Bolzan, L. D. Abreu Sa, H. F. Campos Velho, Phys. A, 295:1–2 (2001), 250–253 | DOI | Zbl

[47] J. R. Bezerra, R. Silva, J. A. S. Lima, Phys. A, 322:1–4 (2003), 256–266, arXiv: cond-mat/0201541 | DOI | MR | Zbl

[48] V. S. Kirchanov, TMF, 156:3 (2008), 444–453 | DOI | MR | Zbl

[49] Z.-H. Feng, L.-Y. Liu, Phys. A, 389:2 (2010), 237–241 | DOI | MR

[50] J. Du, Phys. Lett. A, 329:4–5 (2004), 262–267, arXiv: cond-mat/0404602 | DOI | Zbl

[51] J. Du, Phys. A, 335:1–2 (2004), 107–114 | DOI | MR

[52] R. M. Yulmetyev, F. M. Gafarov, D. G. Yulmetyeva, N. A. Emeljanova, Phys. A, 303:3–4 (2002), 427–438 | DOI | Zbl

[53] R. M. Yulmetyev, N. A. Emelyanova, F. M. Gafarov, Phys. A, 341 (2004), 649–676 | DOI | MR

[54] A. R. Plastino, M. Casas, A. Plastino, Phys. A, 280:3 (2000), 289–303 | DOI

[55] R. K. Niven, Chem. Eng. Sci., 61:11 (2006), 3785–3790 | DOI

[56] G. B. Bagci, Phys. A, 386:1 (2007), 79–84 | DOI

[57] A. G. Bashkirov, A. V. Vityazev, Phys. A, 277:1 (2000), 136–145 | DOI

[58] A. G. Bashkirov, TMF, 149:2 (2006), 299–317 | DOI | DOI | MR | Zbl

[59] P. Jizba, T. Arimitsu, Ann. Phys., 312:1 (2004), 17–59, arXiv: cond-mat/0207707 | DOI | MR | Zbl

[60] A. G. Bashkirov, A. D. Sukhanov, ZhETF, 122:3 (2002), 513–520 | DOI

[61] A. G. Bashkirov, Phys. A, 340:1–3 (2004), 153–162 | DOI | MR

[62] A. S. Parvan, T. S. Biró, Phys. Lett. A, 340:5–6 (2005), 375–387 | DOI | MR | Zbl

[63] A. S. Parvan, T. S. Biró, Phys. Lett. A, 374:19–20 (2010), 1951–1957 | DOI | MR | Zbl

[64] A. Figueiredo, M. A. Amato, T. M. R. Filho, Phys. A, 367 (2006), 191–206 | DOI | MR

[65] R. Luzzi, Á. R. Vasconcellos, J. G. Ramos, Riv. Nuovo Cimento, 30:3 (2007), 95–158 | DOI

[66] Á. R. Vasconcellos, J. G. Ramos, A. Gorenstein, M. U. Kleinke, T. G. Souza Cruz, R. Luzzi, Internat. J. Modern Phys. B, 20:28 (2006), 4821–4841 | DOI | Zbl

[67] A. Vidiella-Barranco, H. Moya-Cessa, Phys. Lett. A, 279:1–2 (2001), 56–60, arXiv: quant-ph/0002071 | DOI | Zbl

[68] G. J. Milburn, Phys. Rev. A, 44:9 (1991), 5401–5406 | DOI | MR

[69] R. Bonifacio, S. Olivares, P. Tombesi, D. Vitali, Phys. Rev. A, 61:5 (2000), 053802, 8 pp., arXiv: quant-ph/9911100 | DOI

[70] G. Kaniadakis, Phys. A, 296:3 (2001), 405–425, arXiv: cond-mat/0103467 | DOI | MR | Zbl

[71] L. Borland, Phys. Rev. E, 57:6 (1998), 6634–6642 | DOI

[72] B. M. Boghosian, Bras. J. Phys., 29:1 (1999), 91–107, arXiv: cond-mat/9812154

[73] M. B. Menskii, UFN, 173:11 (2003), 1199–1219 | DOI

[74] G. Schaller, Non-Equilibrium Master Equations, Tech. Univ., Berlin, 2014

[75] V. V. Sargsyan, Z. Kanokov, G. G. Adamyan, N. V. Antonenko, EChAYa, 41:2 (2010), 330–433 | DOI

[76] S. K. Nemirovskii, Phys. Rep., 524:3 (2013), 85–202 | DOI | MR

[77] G. Lindblad, Commun. Math. Phys., 48:2 (1976), 119–130 | DOI | MR | Zbl

[78] G. Lindblad, Rep. Math. Phys., 10:3 (1976), 393–406 | DOI | MR | Zbl

[79] H. Dekker, Phys. Rep., 80:1 (1981), 1–110 | DOI | MR

[80] A. Isar, A. Sandulescu, H. Scutaru, E. Stefanescu, W. Scheid, Internat. J. Modern Phys. E, 3:2 (1994), 635–714, arXiv: quant-ph/0411189 | DOI | MR

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