Application of the non-extensive statistical approach to high energy particle collisions

In high-energy collisions the number of the created particles is far less than the thermodynamic limit, especially in small colliding systems (e.g. proton-proton). Therefore final-state effects and fluctuations in the one-particle energy distribution are appreciable. As a consequence the characterization of identified hadron spectra with the Boltzmann\,--\,Gibbs thermodynamical approach is insufficient. Instead particle spectra measured in high-energy collisions can be described very well with Tsallis\,--\,Pareto distributions, derived from non-extensive thermodynamics. Using the Tsallis q-entropy formula, a generalization of the Boltzmann\,--\,Gibbs entropy, we interpret the microscopical physics by analysing the Tsallis $q$ and $T$ parameters. In this paper we give a quick overview on these parameters, analyzing identified hadron spectra from recent years in a wide center of mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on this energy and on the particle species. Our findings are described well by a QCD inspired evolution ansatz

Systematic analysis of the non-extensive statistical approach in high energy particle collisions-experiment vs. theory

The analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or nuclear collisions, the number of particles is several orders of magnitude smaller than the Avogadro number; therefore, finite-size and fluctuation effects strongly influence the final-state one-particle energy distributions. Due to the simple characterization, the description of the identified hadron spectra with the Boltzmann-Gibbs thermodynamical approach is insufficient. These spectra can be described very well with Tsallis-Pareto distributions instead, derived from non-extensive thermodynamics. Using the $q$-entropy formula, we interpret the microscopic physics in terms of the Tsallis $q$ and $T$ parameters. In this paper we give a view on these parameters, analyzing identified hadron spectra from recent years in a wide center-of-mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on the center-of-mass energy and particle species (mass). Our findings are described well by a QCD (Quantum Chromodynamics) inspired parton evolution ansatz. Based on this comprehensive study, apart from the evolution, both mesonic and baryonic components found to be non-extensive ($q>1$), besides the mass ordered hierarchy observed in the parameter $T$. We also study and compare in details the theory-obtained parameters for the case of PYTHIA8 Monte Carlo Generator, perturbative QCD and quark coalescence models.Comment: 21 pages, 12 figures. This is an extended version of our paper at the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2016), 10-15 July 2016, Ghent, Belgiu

Pion and Kaon Spectra from Distributed Mass Quark Matter

After discussing some hints for possible masses of quasiparticles in quark matter on the basis of lattice equation of state, we present pion and kaon transverse spectra obtained by recombining quarks with distributed mass and thermal cut power-law momenta as well as fragmenting by NLO pQCD with intrinsic $k_T$ {and nuclear} broadening.Comment: Talk given at SQM 200

Pions and kaons from stringy quark matter

Different hadron transverse momentum spectra are calculated in a non-extensive statistical, quark-coalescence model. For the low-pT part a gluonic string contribution is conjectured, its length distribution and fractality are fitted to RHIC data.Comment: Contribution to SQM2008 (Beijing

Cooper-Frye Formula and Non-extensive Coalescence at RHIC Energy

Transverse spectra are calculated for various types of hadrons stemming from Au Au collisions at $\sqrt{s}=200$ GeV. We utilize a quark recombination model based on generalized Boltzmann-Gibbs thermodynamics for local hadron production at various break-up scenarios.Comment: 4 pages, 1 figur

Near-thermal equilibrium with Tsallis distributions in heavy ion collisions

Hadron yields in high energy heavy ion collisions have been fitted and reproduced by thermal models using standard statistical distributions. These models give insight into the freeze-out conditions at varying beam energies. In this paper we investigate changes to this analysis when the statistical distributions are replaced by Tsallis distributions for hadrons. We investigate the appearance of near-thermal equilibrium state at SPS and RHIC energies. We obtain better fits with smaller chi^2 for the same hadron data, as applied earlier in the thermal fits for SPS energies but not for RHIC energies. This result indicates that at RHIC energies the final state is very well described by a single freeze-out temperature with very little room for fluctuations.Comment: 8 pages, 6 figure

Nonextensive statistical effects in the quark-gluon plasma formation at relativistic heavy-ion collisions energies

We investigate the relativistic equation of state of hadronic matter and quark-gluon plasma at finite temperature and baryon density in the framework of the non-extensive statistical mechanics, characterized by power-law quantum distributions. We impose the Gibbs conditions on the global conservation of baryon number, electric charge and strangeness number. For the hadronic phase, we study an extended relativistic mean-field theoretical model with the inclusion of strange particles (hyperons and mesons). For the quark sector, we employ an extended MIT-Bag model. In this context we focus on the relevance of non-extensive effects in the presence of strange matter.Comment: 12 pages, 5 figure

Consequences of temperature fluctuations in observables measured in high energy collisions

We review the consequences of intrinsic, nonstatistical temperature fluctuations as seen in observables measured in high energy collisions. We do this from the point of view of nonextensive statistics and Tsallis distributions. Particular attention is paid to multiplicity fluctuations as a first consequence of temperature fluctuations, to the equivalence of temperature and volume fluctuations, to the generalized thermodynamic fluctuations relations allowing us to compare fluctuations observed in different parts of phase space, and to the problem of the relation between Tsallis entropy and Tsallis distributions. We also discuss the possible influence of conservation laws on these distributions and provide some examples of how one can get them without considering temperature fluctuations.Comment: Revised version of the invited contribution to The European Physical Journal A (Hadrons and Nuclei) topical issue about 'Relativistic Hydro- and Thermodynamics in Nuclear Physics' guest eds. Tamas S. Biro, Gergely G. Barnafoldi and Peter Va