On thermodynamic self-consistency of generic axiomatic-nonextensive statistics

  • 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 (Tch) and the baryon chemical potential (μb) 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.
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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
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 shu
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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

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 (Tch) and the baryon chemical potential (μb) 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.

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