Abstract
We review the consequences of intrinsic, nonstatistical temperature fluctuations as seen in observables measured in high-energy collisions. We do this from the point of view of nonextensive statistics and Tsallis distributions. Particular attention is paid to multiplicity fluctuations as a first consequence of temperature fluctuations, to the equivalence of temperature and volume fluctuations, to the generalized thermodynamic fluctuations relations allowing us to compare fluctuations observed in different parts of the phase space, and to the problem of the relation between Tsallis entropy and Tsallis distributions. We also discuss the possible influence of conservation laws on these distributions and provide some examples of how one can get them without considering temperature fluctuations.
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References
M. Gazdzicki, M. Gorenstein, P. Seyboth, Acta Phys. Polon. B 42, 307 (2011) and references therein, for example
L. Stodolsky, Phys. Rev. Lett. 75, 1044 (1995)
H. Heiselberg, Phys. Rep. 351, 161 (2001)
S. Mrówczyński, Acta Phys. Polon. B 40, 1053 (2009)
C. Tsallis, Stat. Phys. 52, 479 (1988)
C. Tsallis, Eur. Phys. J. A 40, 257 (2009)
C. Tsallis, Introduction to Nonextensive Statistical Mechanics (Springer, 2009), cf. also
G. Wilk, Z. Włodarczyk, Eur. Phys. J. A 40, 299 (2009)
G. Wilk, Z. Włodarczyk, Phys. Rev. Lett. 84, 2770 (2000)
G. Wilk, Z. Włodarczyk, Chaos Solitons Fractals 13, 581 (2001)
B. De, S. Bhattacharyya, G. Sau, S.K. Biswas, Int. J. Mod. Phys. E 16, 1687 (2007)
C. Alt et al., Phys. Rev. C 77, 034906 (2008)
C. Alt et al., Phys. Rev. C 77, 024903 (2008)
S.V. Afanasiev et al., Phys. Rev. C 66, 054902 (2002)
T.S. Biró, A. Jakovác, Phys. Rev. Lett. 94, 132302 (2005)
T.S. Biró, G. Purcsel, K. Ürmösy, Eur. Phys. J. A 40, 325 (2009)
T.S. Biró, Is there a temperature? Conceptual Challenges at High Energy, Acceleration and Complexity (Springer, 2011)
C. Beck, E.G.D. Cohen, Physica A 322, 267 (2003)
F. Sattin, Eur. Phys. J. B 49, 219 (2006)
G. Wilk, Z. Włodarczyk, Phys. Rev. C 79, 054903 (2009)
G. Wilk, Z. Włodarczyk, Cent. Eur. J. Phys. 8, 726 (2010)
O.J.E. Maroney, Phys. Rev. E 80, 061141 (2009)
T.S. Biró, K. Ürmössy, Z. Schram, J. Phys. G 37, 094027 (2010)
T.S. Biró, P. Ván, Phys. Rev. E 83, 061147 (2011)
T.S. Biró, Z. Schram, Eur. Phys. J. Web Conf. 13, 05004 (2011)
M. Nauenberg, Phys. Rev. E 67, 036114 (2003)
M. Nauenberg, Phys. Rev. E 69, 038102 (2004)
C. Tsallis, Phys. Rev. E 69, 038101 (2004)
R. Balian, M. Nauenberg, Europhys. News 37, 9 (2006)
R. Luzzi et al., Europhys. News 37, 11 (2006)
G. Wilk, Z. Włodarczyk, Cent. Eur. J. Phys. 10, 568 (2012) cf. also arXiv: 1110.4220v2 [hep-ph]
STAR Collaboration (B.I. Abelev et al.), Phys. Rev. C 75, 064901 (2007)
PHENIX Collaboration (A. Adare et al.), Phys. Rev. D 83, 052004 (2011)
CMS Collaboration (V. Khachatryan et al.), JHEP 02, 041 (2010)
CMS Collaboration (V. Khachatryan et al.), Phys. Rev. Lett. 105, 022002 (2010)
ALICE Collaboration (K. Aamodt et al.), Phys. Lett. B 693, 53 (2010)
ALICE Collaboration (K. Aamodt et al.), Eur. Phys. J. C 71, 1594 and 1655 (2011)
ATLAS Collaboration (G. Aad et al.), New J. Phys. 13, 053033 (2011)
Ming Shao, Li Yi, Zebo Tang, Hongfang Chen, Cheng Li, Zhangbu Xu, J. Phys. G 37, 085104 (2010)
J. Cleymans, D. Worku, J. Phys. G 39, 025006 (2012)
T. Osada, G. Wilk, Phys. Rev. C 77, 044903 (2008) Phys. Rev. C 78
T. Osada, G. Wilk, Prog. Theor. Phys. Suppl. 174, 168 (2008)
T. Osada, G. Wilk, Indian J. Phys. 86, 941 (2011)
J. Rozynek, G. Wilk, J. Phys. G 36, 125108 (2009)
J. Rozynek, G. Wilk, Acta Phys. Polon. B 41, 351 (2010)
J. Rozynek, G. Wilk, Eur. Phys. J. Web Conf. 13, 5002 (2011)
G. Wilk, Z. Włodarczyk, Physica A 390, 3566 (2011)
A.K. Dash, B.M. Mohanty, J. Phys. G 37, 025102 (2010)
C. Geich-Gimbel, Int. J. Mod. Phys. A 4, 1527 (1989)
J.F. Grosse-Oetringhaus, K. Reygers, J. Phys. G 37, 083001 (2010)
Z. Koba, H.B. Nielsen, P. Olesen, Nucl. Phys. B 40, 319 (1972)
M. Rybczyński, Z. Włodarczyk, G. Wilk, Nucl. Phys. B Proc. Suppl. 122, 325 (2003)
F.S. Navarra, O.V. Utyuzh, G. Wilk, Z. Włodarczyk, Phys. Rev. D 67, 114002 (2003)
P. Carruthers, C.S. Shih, Int. J. Mod. Phys. A 2, 1447 (1986)
C. Vignat, A. Plastino, Phys. Lett. A 360, 415 (2007)
R.A. Fisher, Ann. Eugenics 11, 182 (1941)
V.V. Begun, M. Gazdzicki, M. Gorenstein, Phys. Rev. C 78, 024904 (2008)
UA5 Collaboration (G.J. Alner et al.), Z. Phys. C 33, 1 (1986)
S. Hegyi, Phys. Lett. B 467, 126 (1999) and in Proc. ISMD2000, Tihany, Lake Balaton, Hungary (2000)
F.S. Navarra, O.V. Utyuzh, G. Wilk, Z. Włodarczyk, Physica A 340, 467 (2004)
F.S. Navarra, O.V. Utyuzh, G. Wilk, Z. Włodarczyk, Physica A 344, 568 (2004)
M. Biyajima, M. Kaneyama, T. Mizoguchi, G. Wilk, Eur. Phys. J. C 40, 243 (2005)
M. Biyajima, T. Mizoguchi, N. Nakajima, N. Suzuki, G. Wilk, Eur. Phys. J. C 48, 593 (2006)
G. Wilk, Z. Włodarczyk, W. Wolak, Acta Phys. Polon. B 42, 1277 (2011)
G. Wilk, Z. Włodarczyk, Physica A 390, 3566 (2011)
N. Bohr, Collected Works, edited by J. Kalekar, Vol. 6 (North-Holland, Amsterdam, 1985) pp. 316-330 and 376-377
J. Lindhard, “Complementarity” between energy and temperature, in The Lesson of Quantum Theory, edited by J. de Boer, E. Dal, O. Ulfbeck (North-Holland, Amsterdam, 1986)
J. Uffink, J. van Lith, Found. Phys. 29, 655 (1999)
J. Uffink, J. van Lith, Thermodynamic uncertainty relations, cond-mat/9806102
B.H. Lavenda, Found. Phys. Lett. 13, 487 (2000)
Kulesh Chandra Kar, Phys. Rev. 21, 672 (1923)
T. Wibig, J. Phys. G 37, 115009 (2010)
G. Wilk, Z. Włodarczyk, PoS WPCF2011, 041 (2011) cf. also arXiv:1202.2711[hep-ph]
G. Wilk, Z. Włodarczyk, Physica A 376, 279 (2007)
J.L. Lebowitz, J.K. Percus, Phys. Rev. 124, 1673 (1961)
J.L. Lebowitz, J.K. Percus, L. Verlet, Phys. Rev. 153, 259 (1967)
R. Guo, J.L. Du, Physica A 391, 2853 (2012)
L.Y. Liu, J.L. Du, Physica A 387, 5417 (2008)
K. Ürmössy, G.G. Barnaföldi, T.S. Biró, Phys. Lett. B 701, 111 (2011)
K. Ürmössy, G.G. Barnaföldi, T.S. Biró, Acta Phys. Polon. B Proc. Suppl. 5, 363 (2012)
G.G. Barnaföldi, T.S. Biró, K. Ürmössy, G. Kalmár, in Proceedings of the Workshop Gribov ’80 (World Scientific, Singapore, 2011)
I.V. Karlin, M. Grmela, N. Gorban, Phys. Rev. E 65, 036128 (2002)
P.N. Rathie, S. Da Silva, Appl. Math. Sci. 2, 1359 (2008)
A. Białas, M. Błeszynski, W. Czyz, Nucl. Phys. B 111, 461 (1976)
K. Fiałkowski, R. Wit, Acta Phys. Polon. B 41, 1317 (2010)
K. Fiałkowski, R. Wit, Eur. Phys. J. A 45, 51 (2010)
PHOBOS Collaboration (B.B. Back et al.), Phys. Rev. C 74, 021902(R) (2006)
T. Oikonomou, G.B. Bagci, Phys. Lett. A 374, 2225 (2010)
C. Tsallis, Physica D 193, 3 (2004)
G.L. Ferri, S. Martinez, A. Plastino, J. Stat. Mech. (2005) P04009
C. Beck, F. Schlögl, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, 1993)
Yu.L. Klimontovich Statistical Theory of Open Systems (Kluwer, Dordrecht, 1995)
C. Tsallis, R.S. Mendes, A.R. Plastino, Physica A 261, 534 (1998)
S. Abe, Phys. Rev. E 66, 046134 (2002)
S. Abe, Astrophys. Space Sci. 305, 241 (2006)
S. Abe, G.B. Bagci, Phys. Rev. E 71, 016139 (2005)
S. Abe, EPL 84, 60006 (2008)
S. Abe, Phys. Rev. E 79, 041116 (2009)
R. Hanel, S. Thurner, C. Tsallis, EPL 85, 20005 (2009)
J.F. Lutsko, J.P. Boon, P. Grosfils, EPL 86, 40005 (2009)
G. Wilk, Z. Włodarczyk, AIP Conf. Proc. 965, 76 (2007) arXiv:0708.2660
H.A. David, Order Statistics (Wiley-InterScience, New York, 1981), or H.A. David, H.N. Nagaraja, Order Statistics, in Wiley Series in Probability and Statistics (Wiley-InterScience, New York, 2003)
P. Castorina, D. Kharzeev, H. Satz, Eur. Phys. J. C 52, 187 (2007)
G. Wilk, Z. Włodarczyk, Acta Phys. Polon. B 35, 871 (2004)
G. Wilk, Z. Włodarczyk, Acta Phys. Polon. B 36, 2513 (2005)
C. Tsallis, Eur. Phys. J. ST 161, 175 (2008)
D.J.B. Soares, C. Tsallis, A.M. Mariz, L.R. da Silva, Europhys. Lett. 70, 70 (2005)
G. Wilk, Z. Włodarczyk, Acta Phys. Polon. B 35, 2141 (2004)
M. Gazdzicki, M.I. Gorenstein, Phys. Lett. B 517, 250 (2001)
S.K. Biswas, G. Sau, A.C. Das Ghosh, S. Bhattacharyya, Open. J. Microphys. 2, 1 (2012)
A.A. Bylinkin, A.A. Rostovtsev, Comparative Analysis of Pion, Kaon and Proton Spectra Produced at PHENIX, arXiv:1203.2840
C. Michael, L. Vanryckeghem, J. Phys. G 3, L151 (1977)
C. Michael, Prog. Part. Nucl. Phys. 2, 1 (1979)
UA1 Collaboration (G. Arnison et al.), Phys. Lett. B 118, 167 (1982)
R. Hagedorn, Riv. Nuovo Cimento 6, 1 (1983)
P. Erdös, A. Rényi, Pub. Math. Inst. Hung. Acad. Sci. 5, 17 (1960)
A.L. Barabási, R. Albert, H. Jeong, Physica A 272, 173 (1999)
R. Albert, H. Jeong, A.L. Barabási, Nature 406, 378 (2000)
R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
T.C.P. Chui, D.R. Swanson, M.J. Adriaans, J.A. Nissen, J.A. Lipa, Phys. Rev. Lett. 69, 3005 (1992)
C. Kittel, Phys. Today 5, 93 (1988)
B.B. Mandelbrot, Phys. Today 42, 71 (1989)
H.B. Prosper, Am. J. Phys. 61, 54 (1993)
G.D.J. Phillies, Am. J. Phys. 52, 629 (1984)
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Wilk, G., Włodarczyk, Z. Consequences of temperature fluctuations in observables measured in high-energy collisions. Eur. Phys. J. A 48, 161 (2012). https://doi.org/10.1140/epja/i2012-12161-y
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DOI: https://doi.org/10.1140/epja/i2012-12161-y