On thermodynamic self-consistency of generic axiomatic-nonextensive statistics

Abdel Nasser Tawfik; Hayam Yassin; Eman R; Abo Elyazeed

doi:10.1088/1674-1137/41/5/053107

Chinese Physics C> 2017, Vol. 41> Issue(5) : 053107 DOI: 10.1088/1674-1137/41/5/053107

On thermodynamic self-consistency of generic axiomatic-nonextensive statistics

1.
Egyptian Center for Theoretical Physics (ECTP), Modern University for Technology and Information (MTI), 11571 Cairo, Egypt
2.
World Laboratory for Cosmology and Particle Physics (WLCAPP), 11571 Cairo, Egypt
3.
Physics Department, Faculty of Women for Arts, Science and Education, Ain Shams University, 11577 Cairo, Egypt

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Abstract：
Generic axiomatic-nonextensive statistics introduces two asymptotic properties, to each of which a scaling function is assigned. The first and second scaling properties are characterized by the exponents c and d, respectively. In the thermodynamic limit, a grand-canonical ensemble can be formulated. The thermodynamic properties of a relativistic ideal gas of hadron resonances are studied, analytically. It is found that this generic statistics satisfies the requirements of the equilibrium thermodynamics. Essential aspects of the thermodynamic self-consistency are clarified. Analytical expressions are proposed for the statistical fits of various transverse momentum distributions measured in most-central collisions at different collision energies and colliding systems. Estimations for the freezeout temperature (T_ch) and the baryon chemical potential (μ_b) and the exponents c and d are determined. The earlier are found compatible with the parameters deduced from Boltzmann-Gibbs (BG) statistics (extensive), while the latter refer to generic nonextensivities. The resulting equivalence class (c,d) is associated with stretched exponentials, where Lambert function reaches its asymptotic stability. In some measurements, the resulting nonextensive entropy is linearly composed on extensive entropies. Apart from power-scaling, the particle ratios and yields are excellent quantities to highlighting whether the particle production takes place (non)extensively. Various particle ratios and yields measured by the STAR experiment in central collisions at 200, 62.4 and 7.7 GeV are fitted with this novel approach. We found that both c and d<1, i.e. referring to neither BG- nor Tsallis-type statistics, but to (c,d)-entropy, where Lambert functions exponentially rise. The freezeout temperature and baryon chemical potential are found comparable with the ones deduced from BG statistics (extensive). We conclude that the particle production at STAR energies is likely a nonextensive process but not necessarily BG or Tsallis type.
- Nonextensive thermodynamical consistency ,
- Boltzmann and Fermi-Dirac statistics

References

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[94]	J. Cleymans, et al., Phys. Lett. B 723:351 (2013)
[95]	G. Wilk and Z. Wlodarczyk, Phys. Rev. Lett. 84:2770 (2000).

References

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[2]	A. Tawfik, J. Phys. G, 40: 055109 (2013)
[3]	R. Hagedorn, Nuovo Cimento Suppl., 3: 147 (1965)
[4]	A. Tawfik, J. Phys. G 40:055109 (2013)
[5]	R. Hagedorn, Nuovo Cimento Suppl. 3:147 (1965)
[6]	A. Tawfik, Prog. Theor. Phys., 126: 279 (2011)
[7]	A. Tawfik, Prog. Theor. Phys. 126:279 (2011)
[8]	C. Beck, Physica, A, 286: 164 (2000)
[9]	I. Bediaga, E. M. F. Curado, and J. M. de Miranda, Physica A, 286: 156 (2000)
[10]	C. Beck, Physica A 286:164 (2000)
[11]	W. M. Alberico, A. Lavagno, and P. Quarati, Eur. Phys. J. C, 12: 499-506 (2000)
[12]	I. Bediaga, E.M.F. Curado and J.M. de Miranda, Physica A 286:156 (2000)
[13]	W. M. Alberico, A. Lavagno, and P. Quarati, Eur. Phys. J. C 12:499-506 (2000)
[14]	S. Tripathy { et al.}, Eur. Phys. J. A, 52: 289 (2016)
[15]	A. Khuntia et al, Eur. Phys. J. A, 52: 292 (2016)
[16]	S. Tripathy, et al., Eur. Phys. J. A 52:289 (2016)
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[18]	A. Khuntia, et al., Eur. Phys. J. A 52:292 (2016)
[19]	A. Deppman, J. Phys. G, 41: 055108 (2014)
[20]	T. Bhattacharyya, et al., Eur. Phys. J. A 52:30 (2016)
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[22]	W. M. Alberico et al, Physica A, 387: 467 (2008)
[23]	W. M. Alberico, et al., Physica A 387:467 (2008)
[24]	T. Bhattacharyya, R. Sahoo, and P. Samantray, Eur. Phys. J. A, 52: 283 (2016)
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[31]	G. Wilk and Z. Wlodarcyk, Phys. Lett. A, 379: 2941 (2015)
[32]	A. Bialas, Phys. Lett. B 747:190 (2015)
[33]	C. Beck and E. G. D. Cohen, Physica A, 322: 267 (2003)
[34]	G. Wilk and Z. Wlodarcyk, Phys. Lett. A 379:2941 (2015)
[35]	C. Beck and E. G. D. Cohen, Physica A 322:267 (2003)
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[51]	A. N. Tawfik, Lattice QCD thermodynamics and RHIC-BES particle production within generic nonextensive statistics, submitted to EPJA
[52]	R. Hanel and S. Thurner, Europhys. Lett. 96:50003 (2011)
[53]	A. S. Parvan, Eur. Phys. J. A, 51: 108 (2015)
[54]	Abdel Nasser Tawfik, Lattice QCD thermodynamics and RHIC-BES particle production within generic nonextensive statistics, submitted to EPJA
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[56]	A. Deppman, Physica A, 391: 6380 (2012)
[57]	A. Deppman, Physica A 391:6380 (2012)
[58]	A. S. Parvan, Phys. Lett. A, 350: 331 (2006)
[59]	A. S. Parvan, Phys. Lett. A, 360: 26 (2006)
[60]	A. S. Parvan, Phys. Lett. A 350:331 (2006)
[61]	A. S. Parvan, Phys. Lett. A 360:26 (2006)
[62]	J. Cleymans and D. Worku, J. Phys. G, 39: 025006 (2012)
[63]	J. Letessier and J. Rafelski, Hadrons and Quark-Gluon Plasma, (Cambridge University Press, UK, 2004), p. 210
[64]	J. Cleymans and D. Worku, J. Phys. G 39:025006 (2012)
[65]	S. Thurner and R. Hanel, Int. J. Mod. Phys.: Conf. series, 16: 105 (2012)
[66]	J. Letessier and J. Rafelski, Hadrons and Quark-Gluon Plasma, (Cambridge University Press, UK, 2004) p. 210
[67]	J. Cleymans, H. Oeschler, K. Redlich, and S. Wheaton, Phys. Rev. C, 73: 034905 (2006)
[68]	S. Thurner and R. Hanel, Int. J. Mod. Phys.:Conf. series 16:105 (2012)
[69]	A. Andronic, P. Braun-Munzinger, and J. Stachel, Nucl. Phys. A, 772: 167 (2006)
[70]	J. Cleymans, H. Oeschler, K. Redlich, and S. Wheaton, Phys. Rev. C 73:034905 (2006)
[71]	A. Andronic, P. Braun-Munzinger, and J. Stachel, Nucl. Phys. A 772:167 (2006)
[72]	F. Becattini, J. Manninen, and M. Gazdzicki, Phys. Rev. C, 73: 044905 (2006)
[73]	C. Albajar et al (UA1 Collaboration), Nucl. Phys. B, 335, 261 (1990)
[74]	F. Becattini, J. Manninen, and M. Gazdzicki, Phys. Rev. C 73:044905 (2006)
[75]	A. Adare et al (PHENIX Collaboration), Phys. Rev. C, 88: 024906 (2013)
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[77]	B. I. Abelev et al (STAR Collaboration), Phys. Rev. C, 79: 034909 (2009)
[78]	A. Adare, et al. (PHENIX Collaboration), Phys. Rev. C 88:024906 (2013)
[79]	B. Abelev et al (ALICE Collaboration), Phys. Lett. B, 728: 25 (2014)
[80]	B. I. Abelev, et al. (STAR Collaboration), Phys. Rev. C 79:034909 (2009)
[81]	B. Abelev, et al. (ALICE Collaboration), Phys. Lett. B 728:25 (2014)
[82]	B. Abelev et al (ALICE Collaboration), Phys. Rev. Lett. 109: 252301 (2012)
[83]	A. N. Tawfik and E. Abbas, Phys. Part. Nucl. Lett., 12: 521 (2015)
[84]	B. Abelev, et al. (ALICE Collaboration), Phys. Rev. Lett. 109:252301 (2012)
[85]	Abdel Nasser Tawfik and Ehab Abbas, Phys. Part. Nucl. Lett. 12:521 (2015)
[86]	C. Anteneodo and A. R. Plastino, J. Phys A: Math. Gen., 32: 1089 (1999)
[87]	C. Anteneodo and A. R. Plastino. J. Phys A:Math. Gen. 32:1089 (1999).
[88]	R. Hanel and S. Thurner, arXir: 1005.0138 [physics.class-ph]
[89]	R. Hanel and S. Thurner, A classification of complex statistical systems in terms of their stability and a thermodynamical derivation of their entropy and distribution functions, 1005.0138[physics.class-ph].
[90]	Fariel Shafee, IMA J. Appl. Math., 72: 785 (2007)
[91]	Fariel Shafee, IMA J. Appl. Math. 72:785 (2007).
[92]	J. Cleymans et al, Phys. Lett. B, 723: 351 (2013)
[93]	G. Wilk and Z. Wlodarczyk, Phys. Rev. Lett., 84: 2770 (2000)l Nasser Tawfik, Int. J. Mod. Phys. A 29:1430021 (2014)
[94]	J. Cleymans, et al., Phys. Lett. B 723:351 (2013)
[95]	G. Wilk and Z. Wlodarczyk, Phys. Rev. Lett. 84:2770 (2000).

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Abdel Nasser Tawfik, Hayam Yassin, Eman R and Abo Elyazeed. On thermodynamic self-consistency of generic axiomatic-nonextensive statistics[J]. Chinese Physics C, 2017, 41(5): 053107. doi: 10.1088/1674-1137/41/5/053107

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Received: 2016-12-21
Revised: 2016-12-23

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沈阳化工大学材料科学与工程学院沈阳 110142

On thermodynamic self-consistency of generic axiomatic-nonextensive statistics

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