Self-consistent thermodynamics for the Tsallis statistics in the grand canonical ensemble: Nonrelativistic hadron gas

In the present paper, the Tsallis statistics in the grand canonical ensemble was reconsidered in a general form. The thermodynamic properties of the nonrelativistic ideal gas of hadrons in the grand canonical ensemble was studied numerically and analytically in a finite volume and the thermodynamic limit. It was proved that the Tsallis statistics in the grand canonical ensemble satisfies the requirements of the equilibrium thermodynamics in the thermodynamic limit if the thermodynamic potential is a homogeneous function of the first order with respect to the extensive variables of state of the system and the entropic variable $z=1/(q-1)$ is an extensive variable of state. The equivalence of canonical, microcanonical and grand canonical ensembles for the nonrelativistic ideal gas of hadrons was demonstrated.Comment: 8 figure

Comparison of Tsallis statistics with the Tsallis-factorized statistics in the ultrarelativistic pppp collisions

The Tsallis statistics was applied to describe the experimental data on the transverse momentum distributions of hadrons. We considered the energy dependence of the parameters of the Tsallis-factorized statistics, which is now widely used for the description of the experimental transverse momentum distributions of hadrons, and the Tsallis statistics for the charged pions produced in $pp$ collisions at high energies. We found that the results of the Tsallis-factorized statistics deviate from the results of the Tsallis statistics only at low NA61/SHINE energies when the value of the entropic parameter is close to unity. At higher energies, when the value of the entropic parameter deviates essentially from unity, the Tsallis-factorized statistics satisfactorily recovers the results of the Tsallis statistics.Comment: 8 figures. arXiv admin note: text overlap with arXiv:1607.0195

Scaled variables and the quark-hadron duality

The thermodynamic quantities of the ideal gas of hadrons and the $(2+1)$--flavor lattice QCD scaled by the effective degeneracy factors of the corresponding models are compared. We have found that in terms of the scaled variables the quark-hadron duality of the lattice QCD and the hadron resonance gas (HRG) model disappears. However, we have unexpectedly revealed that the scaled variables lead to the quark-hadron duality of the lattice QCD and the quantum ideal gas of kaons and antikaons, namely, the ideal gas of those hadrons that contain all the three quarks $u,d,s$ and their antiquarks. Satisfactory agreement between the scaled results of the kaon ideal gas and the lattice QCD data is achieved at large values of the volume in the entire temperature range. In the ideal gas of kaons there is no any phase transition. Nevertheless, in our calculations the scaled thermodynamic quantities of the ideal gas and the lattice QCD follow the same qualitative behavior and are consistent with each other especially at high temperatures in the perturbative region.Comment: 3 figure