On thermodynamic self-consistency of generic axiomatic-nonextensive statistics

Abstract

Generic axiomatic-nonextensive statistics characterized by two asymptotic properties, to each of them a scaling function is assigned, characterized by the exponents c and d for first and second scaling property, respectively, is formulated in a grand-canonical ensemble with finite volume in the thermodynamic limit. 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 to 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 raise. 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.

Transverse momentum spectra of strange hadrons within extensive and nonextensive statistics

“…The enhancement of the strangeness number [7,8] and of the transverse momentum p T spectra of strange particles [9] are well-known examples. The importance of the latter is the ability to determine the freezeout parameters; the temperature and the chemical potential in different statistical approaches [10][11][12][13][14][15][16]. These statistical models are able to describe the experimental results, at a wide range of energies [6].…”

“…The generic (non)extensive approach, which was introduced in ref. [23] and utilized in estimating the particle production, at a wide range of energies [24][25][26] was utilized to analyze the p T spectra of charged particles measured in different types of collisions at RHIC and LHC energies [16,43]. This motivates the present work, in which p T of strange hadrons are fitted to extensive (Boltzmann) and nonextensive approaches [Tsallis and generic (non)extensive], at various energies.…”

Transverse momentum $p_{\mathrm{T}}$ spectra of strange particles production in different collisions at $\sqrt{s_{NN}}= 2.76, 5.02,$ and $7$ TeV

“…Also, another important indication for the formation of QGP is the transverse momentum p T spectra of the charged and strange particles [10]. Because the p T spectra can give information about the chemical freezeout -chemical potential and temperature -by utilizing many statistical models [11,12,13,14,15,16,17]. These statistical models describe the experimental measurements over a wide range of center-of-mass energies depending on different statistics.…”

Extensive/nonextensive statistics for $p_T$ distributions of various charged particles produced in p+p and A+A collisions in a wide range of energies

“…To remain within the scope of the present research paper, we intentionally disregard the recent proposal that the degree of nonextensivity can be best taken into account when -instead of this types of nonextensivity -a wider class of superstatistics should be implemented, e.g. generic axiomatic nonextensive approach [25][26][27], where both Boltzmann-Gibbs (BG) and Tsallis approaches represent very special cases in it.…”

“…For example, if the answer to the last question, for instance, is "yes", one would expect that other aspects of the particle production, such as the particle multiplicity (particle yields and their ratios) could (should) be reproduced by Tsallis statistics, as well. Apparently, this is not the case [25,27,41]! The transverse momentum (p T ) quantifies the projection of the four-momentum onto the plane with a transverse (perpendicular) orientation to the collision axis (z-axis).…”