The proposed analogy between hadron production in high-energy collisions and Hawking-Unruh radiation process in the black holes shall be extended. This mechanism provides a theoretical basis for the freeze-out parameters, the temperature (T ) and the baryon chemical potential (µ), characterizing the final state of particle production. The results from charged black holes, in which the electric charge is related to µ, are found comparable with the phenomenologically deduced parameters from the ratios of various particle species and the higher-order moments of net-proton multiplicity in thermal statistical models and Polyakov linear-sigma model. Furthermore, the resulting freeze-out condition E / N ≃ 1 GeV for average energy per particle is in good agreement with the hadronization process in the high-energy experiments. For the entropy density (s), the freeze-out condition s/T 3 ≃ 7 remains valid for µ < ∼ 0.3 GeV. Then, due to the dependence of T on µ, the values of s/T 3 increase with increasing µ. In accordance with this observation, we found that the entropy density remains constant with increasing µ. Thus, we conclude that almost no information is going lost throughHawking-Unruh radiation from charged black holes. It is worthwhile to highlight that the freeze-out temperature from charged black holes is determined independent on both freeze-out conditions.

The particle production in relativistic heavy-ion collisions seems to be created in a dynamically disordered system which can be best described by an extended exponential entropy. In distinguishing between the applicability of this and Boltzmann-Gibbs (BG) in generating various particle-ratios, generic (non)extensive statistics (GNS) is introduced to the hadron resonance gas model. Accordingly, the degree of (non)extensivity is determined by the possible modifications in the phase space. Both BG extensivity and Tsallis nonextensivity are included as very special cases defined by specific values of the equivalence classes (c, d). We found that the particle ratios at energies ranging between 3.8 and 2760 GeV are best reproduced by nonextensive statistics, where c and d range between ∼ 0.9 and ∼ 1. The present work aims at illustrating that the proposed approach is well capable to manifest the statistical nature of the system on interest. We don't aim at highlighting deeper physical insights. In other words, while the resulting nonextensivity is neither BG nor Tsallis, the freezeout parameters are found very compatible with BG and accordingly with the well-known freezeout phase-diagram, which is in an excellent agreement with recent lattice calculations. We conclude that the particle production is nonextensive but should not necessarily be accompanied by a radical change in the intensive or extensive thermodynamic quantities, such as internal energy and temperature. Only, the two critical exponents defining the equivalence classes (c, d) are the physical parameters characterizing the (non)extensivity.1 particle productions, even at the kinetic freezeout [9,10,11,12,13]. The long-range fluctuations, the correlations, and the interactions besides the possible modifications in the phase space of the particle production are not properly incorporated through Tsallis algebra. In long-range interactions, both thermodynamic and long-time limits do not commute. Therefore, generic nonextensive statistics (GNS) was introduced in Ref. [9,10,11], in which the phase space becomes responsible in determining the degree of (non)extensivity. It was shown that the lattice thermodynamics is well reproduced when the proposed GNS become characterized by extensive critical exponents (1, 1), while the heavy-ion particle ratios are only reproduced when the proposed GNS become nonextensive critical exponents, e.g. neither 0 nor 1. The latter differs from Tsallis [9,10,11]. Nonextensive statistics becomes the relevant approach for nonequilibrium stationary states. While zeroth law of thermodynamics in equilibrium introduces "the temperature", a so-called "physical temperature" was proposed when utilizing Tsallis-algebra, see for instance [14,15,16,17]. It was concluded that if the inverse Lagrange multiplier associated with constrained internal energy is regarded as "the temperature", both Tsallis and Clausius entropies become identical. This temperature is believed to differ from the "physical" one. Based on this assumption, the "physical te...

PACS 25.75.-q -Relativistic heavy-ion nuclear reactions PACS 25.75.Dw -Particle production (relativistic collisions) PACS 24.85.+p -Quantum chromodynamics in nuclei Abstract -The strange-quark occupation factor (γs) is determined from the statistical fit of the multiplicity ratio K + /π + in a wide range of nucleon-nucleon center-of-mass energies ( √ sNN ).From this single-strange-quark-subsystem, γs( √ sNN ) was parametrized as a damped trigonometric functionality and successfully implemented to the hadron resonance gas model, at chemical semi-equilibrium. Various particle ratios including K − /π − , Λ/π − , andΛ/π − are well reproduced. The phenomenology of γs( √ sNN ) suggests that, the hadrons (γs raises) at √ sNN ≃ 7 GeV seems to undergo a phase transition to a mixed phase (γs declines), which is then derived into partons (γs remains unchanged with increasing √ sNN ), at √ sNN ≃ 20 GeV.

This letter presents an extension of EPL116(2017)62001 to light-and strange-quark nonequilibrium chemical phase-space occupancy factors (γ q,s ). The resulting damped trigonometric functionalities relating γ q,s to the nucleon-nucleon center-of-mass energies ( √ s N N ) looks very similar except different coefficients. The phenomenology of the resulting γ q,s ( √ s N N ) describes a rapid decrease at √ s N N < ∼ 7 GeV followed by a faster increase up to ∼ 20 GeV. Then, both γ q,s become nonsensitive to √ s N N .Although these differ from γ s ( √ s N N ) obtained at γ q ( √ s N N ) = 1, various particle ratios including K + /π + , K − /π − , Λ/π − ,Λ/π − , Ξ + /π + , and Ω/π − , can well be reproduced, as well. We conclude that γ q,s ( √ s N N ) should be instead determined from fits of various particle yields and ratios but not merely from fits to the particle ratio K + /π + .

The assumption that the production of quark-antiquark pairs and their sequential string-breaking taking place through the event horizon of the color confinement determines freezeout temperature and gives a plausible interpretation of the thermal pattern of pp and AA collisions. When relating the black-hole electric charges to the baryon-chemical potentials it was found that the phenomenologicallydeduced parameters from various particle ratios in the statistical thermal models agree well with the ones determined from the thermal radiation from charged black-hole. Accordingly, the resulting freezeout conditions, such as s/T 3 = 7 and < E > / < N >= 1 GeV, are confirmed at finite chemical potentials, as well. Furthermore, the problematic of strangeness production in elementary collisions can be interpreted by thermal particle production from the Hawking-Unruh radiation. Consequently, the freezeout temperature depends on the quark masses. This leads to a deviation from full equilibrium and thus a suppression of the strangeness production in the elementary collisions. But in nucleus-nucleus collisions, an average temperature should be introduced in order to dilute the quark masses. This nearly removes the strangeness suppression. An extension to finite chemical potentials is introduced. The particle ratios of kaon-to-pion, phi-to-kaon and antilambda-to-pion are determined from Hawking-Unruh radiation and compared with the thermal calculations and the measurements in different experiments. We conclude that these particle ratios can be reproduced, at least qualitatively, as Hawking-Unruh radiation at finite chemical potential. With increasing energy, both K+/pi+ and phi/K-keep their maximum values at low SPS energies. But the further energy decrease rapidly reduces both ratios. For Lambda/pi-, there is an increase with increasing collision energy, i.e. no saturation is to be observed.