Abstract
By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is shown that the power-law distributions describe the long-range nature of the interactions and the non-local correlations within the self-gravitating system with the inhomogeneous velocity dispersion. A relation is established between the nonextensive parameter q≠1 and the measurable quantities of the self-gravitating system: the velocity dispersion and the mass density. Correspondingly, the nonextensive parameter q can be uniquely determined from the microscopic dynamical equation and thus the physical interpretation of q different from unity can be clearly presented. We derive a nonlinear differential equation for the radial density dependence of the self-gravitating system with the inhomogeneous velocity dispersion, which can correctly describe the density distribution for the dark matter in the above physical situation. We also apply this q-kinetic approach to analyze the nonextensivity of self-gravitating collisionless systems and self-gravitating gaseous dynamical systems, giving the power-law distributions the clear physical meaning.
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References
Abe, S., Okamoto, Y.: Nonextensive Statistical Mechanics and its Applications. Springer, Berlin (2001)
Abe, S., Tirmakli, U., Varotsos, P.A.: Europhys. News 36, 206 (2005)
Almeida, M.P.: Physica A 300, 424 (2001)
Baranger, M.: Physica A 305, 27 (2002)
Binney, J., Tremaine, S.: Galactic Dynamics. Princeton University Press, Princeton (1987)
Boon, J.P., Tsallis, C.: Europhys. News 36, 185 (2005)
Chandrasekhar, S.: An Introduction to the Theory of Stellar Structure. Dover, New York (1942)
Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-uniform Gases. Cambridge University Press, Cambridge (1970)
Chavanis, P.H.: Physica A 365, 102 (2006)
Chavanis, P.H., Sire, C.: Physica A 356, 419 (2005)
Cohen, E.G.D.: Physica A 305, 19 (2002)
Du, J.L.: Europhys. Lett. 67, 893 (2004a)
Du, J.L.: Phys. Lett. A 329, 262 (2004b)
Du, J.L.: Phys. Lett. A 320, 347 (2004c)
Du, J.L.: Physica A 335, 107 (2004d)
Du, J.L.: Central Eur. J. Phys. 3, 376 (2005)
Du, J.L.: New Astron. 12, 60 (2006a)
Du, J.L.: Europhys. Lett. 75, 861 (2006b)
Du, J.L.: Astrophys. Space Sci. 305, 247 (2006c)
Gell-Mann, M., Tsallis, C.: Nonextensive Entropy—Interdisciplinary Applications. Oxford University Press, New York (2004)
Lavagno, A., Quarati, P.: Astrophys. Space Sci. 305, 253 (2006)
Leubner, M.P.: Astrophys. J. 604, 469 (2004)
Leubner, M.P.: Astrophys. J. 632, L1 (2005)
Leubner, M.P., Voros, Z.: Astrophys. J. 618, 547 (2004)
Lima, J.A.S., Souza, R.E.: Physica A 350, 303 (2005)
Lima, J.A.S., Silva, R., Santos, J.: Phys. Rev. E 61, 3260 (2000)
Lima, J.A.S., Silva, R., Plastino, A.R.: Phys. Rev. Lett. 86, 2938 (2001)
Lima, J.A.S., Silva, R., Santos, J.: Astron. Astrophys. 396, 309 (2002)
Plastino, A.: Physica A 344, 608 (2004)
Plastino, A.R.: Europhys. News 36, 208 (2005)
Plastino, A.R., Plastino, A.: Phys. Lett. A 174, 384 (1993)
Pluchino, A., Latora, V., Rapisarda, A.: Cont. Mech. Thermodyn. 16, 245 (2004)
Sakagami, M., Taruya, A.: Cont. Mech. Thermodyn. 16, 279 (2004)
Shaikh, S., Khan, A., Bhatia, P.K.: Z. Naturforsch. 61a, 275 (2006)
Silva, R., Plastino, A.R., Lima, J.A.S.: Phys. Lett. A 249, 401 (1998)
Tamarit, F.A., Anteneodo, C.: Europhys. News 36, 194 (2005)
Taruya, A., Sakagami, M.: Physica A 307, 185 (2002)
Tsallis, C.: J. Stat. Phys. 52, 479 (1988)
Tsallis, C.: Physica A 340, 1 (2004)
Tsallis, C., Borges, E.P., Baldovia, F.: Physica A 305, 1 (2002)
Tsallis, C., Brigatti, E.: Cont. Mech. Thermodyn. 16, 223 (2004)
Tsallis, C., Gell-Mann, M., Sato, Y.: Europhys. News 36, 186 (2005)
Wang, Z.X.: The Introduction to Statistical Physics. The People’s Education Press, Beijing (1978)
Wuensche, C.A., Ribeiro, A.L.B., Ramos, F.M., Rosa, R.R.: Physica A 344, 743 (2004)
Wu, J.L., Chen, H.J.: Phys. Scr. 75, 722 (2007)
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Jiulin, D. Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactions. Astrophys Space Sci 312, 47–55 (2007). https://doi.org/10.1007/s10509-007-9611-8
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DOI: https://doi.org/10.1007/s10509-007-9611-8