On thermodynamic self-consistency of generic axiomatic-nonextensive statistics

Generic axiomatic-nonextensive statistics characterized by two asymptotic properties, to each of them a scaling function is assigned, characterized by 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. It is found that this generic statistics satisfies the requirements of the equilibrium thermodynamics. Essential aspects of 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 and chemical potential and both 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 nonextensivity. 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 of 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 to 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. We conclude that the particle production at STAR energies is likely a nonextensive process but not necessarily BG or Tsallis type.