Abstract
Self-gravitating systems are non-equilibrium a priori. A new approach is proposed, which employs a non-equilibrium statistical operator that takes account inhomogeneous distribution of particles and temperature. The method involves a saddle-point procedure to find the dominant contributions to the partition function, thus obtaining all thermodynamic parameters of the system. Probable peculiar features in the behavior of the self-gravitating systems are considered for various conditions. The equation of state for self-gravitating systems has been determined. A new length of the statistical instability is obtained for a real gravitational system, as are parameters of the spatially inhomogeneous distribution of particles and temperature.
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References
P.-H. Chavanis, Int. J. Mod. Phys. B 20, 3113 (2006)
T. Padmanabhan, Phys. Report 188, 285 (1990)
W.C. Saslow, Gravitational physics of stellar and galactic system (Cambridge University Press, New York, 1987)
S. Chandrasekhar, An introduction to the theory of a cellar structure (Dover Publication, New York, 1942)
W. Thirring, Z. Phys. 235, 339, (1970)
P.-H. Chavanis, Phys. Rev. E 65, 056123 (2002)
C. Sire, P.-H. Chavanis, Phys. Rev. E 66, 046133 (2002)
H.J. de Vega, N. Sanchez, Phys. Lett. B 490, 180 (2000)
H.J. de Vega, N. Sanchez, Nucl. Phys. B 625, 409 (2002)
H.J. de Vega, N. Sanchez, Nucl. Phys. B 625, 460 (2002)
D. Ruelle, Statistical Mechanics. Rigorous Results (W.A. Benjamin Inc., New York, Amsterdam, 1969)
G. Rybicki, Astrophys. Space Sci. 14, 56 (1971)
K.R. Yawn, B.N. Miller, Phys. Rev. E 68, 056120 (2003)
J.J. Aly, Phys. Rev. E 39, 3771 (1994)
V. Laliena, Nucl. Phys. B 668, 403 (2003)
Y.D. Bilotsky, B.I. Lev, Teor. Math. Fiz 60, 120 (1984)
B.I. Lev, A.Ya. Zhugaevych, Phys. Rev. E57, 6460 (1998)
H. Kleinert, Gauge Field in Condensed Matter (Word Scientific, Singapore, 4989)
R.L. Stratonovich, Sov. Phys. Dokl. 9, 416 (1984)
K.V. Grigorishin, B.I. Lev, Phys. Rev. E 71, 066105 (2005)
Y. Levin, R. Pakter, F.B. Rizzato, T.N. Teles, F.P.C. Benetti, Phys. Rep. 535, 1 (2004)
R. Pakter, B. Marcos, Y. Levin, Phys. Rev. Lett. 111, 230603 (2013)
F.P.C. Benetti, A.C. Ribeiro-Teixeira, R. Pakter, Y. Levin, Phys. Rev. Lett. 113, 100602 (2014)
M. Joyce, T. Worrakitpoonpon, J. Stat. Mech. 2010, P10012 (2010)
R. Michie, MNRAS 125, 127M (1963)
R. Michie, P.H. Bodenheimer, MNRAS 126, 269M (1963)
R. Baxter, Exactly Solved Models in Statistical Mechanics (Acad. Press, New York, 1980)
W. Jaffe, MNRAS 202, 995J (1983)
D.N. Zubarev, Non-equilibrium statistical thermodynamics (Consultants Bureau, New York, 1974)
K. Huang, Statistical Mechanics (J. Wiley and Sons, New York, 1963)
A. Isihara, Statistical Mechanics (State University of New York, 1971)
H.J. de Vega, N. Sanchez, F. Combes, Phys. Rev. D 54, 6008 (1996)
H.J. de Vega, N. Sanchez, Phys. Lett. B 490, 180 (2000)
J.A.S. Lima, R. Silva, J. Santos, Astron. Astrophys. 396, 309 (2002)
A.P. Boss, Science 276, 1836 (1997)
S. Michael Fall, Ann. New York Acad. Sci. 336, 172 (2006)
B.I. Lev, Int. J. Mod. Phys. B 25, 2237 (2011)
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Lev, S.B., Lev, B.I. Statistical description of nonequilibrium self-gravitating systems. Eur. Phys. J. B 90, 3 (2017). https://doi.org/10.1140/epjb/e2016-70386-9
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DOI: https://doi.org/10.1140/epjb/e2016-70386-9