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

Caloric curve for nuclear liquid-gas phase transition in relativistic mean-field hadronic model

The main thermodynamical properties of the first order phase transition of the relativistic mean-field (RMF) hadronic model were explored in the isobaric, the canonical and the grand canonical ensembles on the basis of the method of the thermodynamical potentials and their first derivatives. It was proved that the first order phase transition of the RMF model is the liquid-gas type one associated with the Gibbs free energy $G$. The thermodynamical potential $G$ is the piecewise smooth function and its first order partial derivatives with respect to variables of state are the piecewise continuous functions. We have found that the energy in the caloric curve is discontinuous in the isobaric and the grand canonical ensembles at fixed values of the pressure and the chemical potential, respectively, and it is continuous, i.e. it has no plateau, in the canonical and microcanonical ensembles at fixed values of baryon density, while the baryon density in the isotherms is discontinuous in the isobaric and the canonical ensembles at fixed values of the temperature. The general criterion for the nuclear liquid-gas phase transition in the canonical ensemble was identified

Finite size effects in the thermodynamics of a free neutral scalar field

The exact analytical lattice results for the partition function of the free neutral scalar field in one spatial dimension in both the configuration and the momentum space were obtained in the framework of the path integral method. The symmetric square matrices of the bilinear forms on the vector space of fields in both configuration space and momentum space were found explicitly. The exact lattice results for the partition function were generalized to the three-dimensional spatial momentum space and the main thermodynamic quantities were derived both on the lattice and in the continuum limit. The thermodynamic properties and the finite volume corrections to the thermodynamic quantities of the free real scalar field were studied. We found that on the finite lattice the exact lattice results for the free massive neutral scalar field agree with the continuum limit only in the region of small values of temperature and volume. However, at these temperatures and volumes the continuum physical quantities for both massive and massless scalar field deviate essentially from their thermodynamic limit values and recover them only at high temperatures or/and large volumes in the thermodynamic limit.Comment: 9 figures, accepted for publicatio

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

Non-extensivity of the QCD pT spectra

We try to establish a connection between the hadronic distributions, in proton-proton collisions at very high transverse momentum $p_{\mathrm{T}}$, obtained via perturbative QCD and the Tsallis non extensive statistics. Our motivation is that while the former is expected to be valid at extremely high momentum, due to asymptotic freedom, the latter has been very successful in describing experimental spectra over a wide range of momentum. Matching the non extensive statistics with the asymptotic $p_{\mathrm{T}}$ behaviour expected from QCD leads to the value of $q=1.25$.Comment: 4 page

The Renyi entropy H_2 as a rigorous, measurable lower bound for the entropy of the interaction region in multiparticle production processes

A model-independent lower bound on the entropy S of the multiparticle system produced in high energy collisions, provided by the Renyi entropy H_2, is shown to be very effective. Estimates show that the ratio H_2/S remains close to one half for all realistic values of the parameters.Comment: Eur. Phys. J. C in print, 17 pages, 5 figure