Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results

Journal

2009 | 7 | 3 | 405-413

Article title

The q-exponential family in statistical physics

Authors

Content

Title variants

Languages of publication

EN

Abstracts

EN
The notion of a generalized exponential family is considered in the restricted context of non-extensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the micro-canonical ensemble belong to the q-exponential family.

Contributors

author
  • Departement Natuurkunde, Universiteit Antwerpen, Universiteitsplein 1, 2610, Antwerpen, Belgium

References

  • [1] J. Naudts, J. Ineq. Pure Appl. Math. 5, 102 (2004)
  • [2] J. Naudts, Open Syst. Inf. Dyn. 12, 13 (2005) http://dx.doi.org/10.1007/s11080-005-0483-5[Crossref]
  • [3] J. Naudts, Physica A 365, 42 (2006) http://dx.doi.org/10.1016/j.physa.2006.01.019[Crossref]
  • [4] J. Naudts, Entropy 10, 131 (2008) http://dx.doi.org/10.3390/entropy-e10030131[Crossref]
  • [5] P.D. Grünwald, A.P. Dawid, Ann. Stat. 32, 1367 (2004) http://dx.doi.org/10.1214/009053604000000553[Crossref]
  • [6] S. Eguchi, Sugaku Expositions 19, 197 (2006) (originally S_ugaku 56, 380 (2004) in Japanese)
  • [7] T.D. Sears, S.V.N. Vishwanathan, Fenchel duality and Generalized maxent, submitted to SIAM Review (2007)
  • [8] S. Abe, J. Phys. A 36, 8733 (2003) http://dx.doi.org/10.1088/0305-4470/36/33/301[Crossref]
  • [9] R. Hanel, S. Thurner, Physica A 380, 109 (2007) http://dx.doi.org/10.1016/j.physa.2007.02.070[Crossref]
  • [10] C. Tsallis, J. Stat. Phys. 52, 479 (1988) http://dx.doi.org/10.1007/BF01016429[Crossref]
  • [11] C. Tsallis, In: M. Gell-Mann, C. Tsallis (Eds.), Nonextensive Entropy (Oxford University Press, Oxford, 2004) 1
  • [12] C. Tsallis, Quim. Nova 17, 468 (1994)
  • [13] J. Naudts, Physica A 316, 323 (2002) http://dx.doi.org/10.1016/S0378-4371(02)01018-X[Crossref]
  • [14] L.G. Moyano, C. Tsallis, M. Gell-Mann, Europhys. Lett. 73, 813 (2006) http://dx.doi.org/10.1209/epl/i2005-10487-1[Crossref]
  • [15] H.J. Hilhorst, G. Schehr, J. Stat. Mech. P06003 (2007)
  • [16] S. Umarov, C. Tsallis, AIP Conf. Proc. 965, 34 (2007) http://dx.doi.org/10.1063/1.2828756[Crossref]
  • [17] C. Vignat, A. Plastino, J. Phys. A 40, F969 (2007) http://dx.doi.org/10.1088/1751-8113/40/45/F02[Crossref]
  • [18] C. Vignat, A. Plastino, Phys. Lett. A 365, 370 (2007) http://dx.doi.org/10.1016/j.physleta.2007.02.003[Crossref]
  • [19] N. Meyer-Vernet, M. Moncuquet, S. Hoang, Icarus 116, 202 (1995) http://dx.doi.org/10.1006/icar.1995.1121[Crossref]
  • [20] D. Ruelle, Statistical mechanics, Rigorous results (W.A. Benjamin, Inc., New York, 1969)
  • [21] R. Hanel, S. Thurner, AIP Conf. Proc. 965, 68 (2007) http://dx.doi.org/10.1063/1.2828761[Crossref]
  • [22] S. Amari, Differential-geometrical methods in statistics Lecture Notes in Statistics 28 (Springer, New York, Berlin, 1985)
  • [23] M.K. Murray, J.W. Rice, Differential geometry and statistics (Chapman and Hall, 1993)
  • [24] A. Ohara, Phys. Lett. A 370, 184 (2007) http://dx.doi.org/10.1016/j.physleta.2007.05.104[Crossref]
  • [25] S. Abe, Physica A 368, 430 (2006) http://dx.doi.org/10.1016/j.physa.2006.04.001[Crossref]
  • [26] A. Plastino, A.R. Plastino, H.G. Miller, Physica A 235, 577 (1997) http://dx.doi.org/10.1016/S0378-4371(96)00386-X[Crossref]
  • [27] F. Pennini, A. Plastino, Physica A 247, 559 (1997) http://dx.doi.org/10.1016/S0378-4371(97)00395-6[Crossref]
  • [28] C. Tsallis, Phys. Rev. E 58, 1442 (1998) http://dx.doi.org/10.1103/PhysRevE.58.1442[Crossref]
  • [29] L. Borland, A. R. Plastino, C. Tsallis, J. Math. Phys. 39, 6490 (1998); Erratum 40, 2196 (1999) http://dx.doi.org/10.1063/1.532660[Crossref]
  • [30] F. Pennini, A. Plastino, Physica A 334, 132 (2004) http://dx.doi.org/10.1016/j.physa.2003.10.076[Crossref]
  • [31] F. Pennini, A. Plastino, Phys. Lett. A 326, 20 (2004) http://dx.doi.org/10.1016/j.physleta.2004.04.024[Crossref]
  • [32] C. Tsallis, R.S. Mendes, A.R. Plastino, Physica A 261, 543 (1998) http://dx.doi.org/10.1016/S0378-4371(98)00437-3[Crossref]
  • [33] H. Hasegawa, Rep. Math. Phys. 33, 87 (1993) http://dx.doi.org/10.1016/0034-4877(93)90043-E[Crossref]
  • [34] G. Pistone, C. Sempi, Ann. Statist. 23, 1543 (1995) http://dx.doi.org/10.1214/aos/1176324311[Crossref]
  • [35] A. Ohara, T. Wada, arXiv:0810.0624 [WoS]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-008-0150-x
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.