Chiral Phase Transition in Linear Sigma Model with Nonextensive Statistical Mechanics

Shen, Ke-Ming; Zhang, Hui; Hou, Defu; Zhang, Ben-Wei; Wang, Enke

doi:10.1155/2017/4135329

Cited by 16 publications

(23 citation statements)

References 29 publications

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“…We now discuss the chemical potential

of the i -th parton. Generally, the chemical potential

of a particle obviously affects the particle production at low energy [ 52 , 53 , 54 , 55 , 56 , 57 , 58 ]. For baryons (mostly protons and neutrons), the chemical potential

related to collision energy

is empirically given by

where both

and

are in the units of GeV [ 59 , 60 , 61 ].…”

Section: Formalism and Methodsmentioning

confidence: 99%

Excitation Functions of Tsallis-Like Parameters in High-Energy Nucleus–Nucleus Collisions

Liu

Olimov

2021

Entropy

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The transverse momentum spectra of charged pions, kaons, and protons produced at mid-rapidity in central nucleus–nucleus (AA) collisions at high energies are analyzed by considering particles to be created from two participant partons, which are assumed to be contributors from the collision system. Each participant (contributor) parton is assumed to contribute to the transverse momentum by a Tsallis-like function. The contributions of the two participant partons are regarded as the two components of transverse momentum of the identified particle. The experimental data measured in high-energy AA collisions by international collaborations are studied. The excitation functions of kinetic freeze-out temperature and transverse flow velocity are extracted. The two parameters increase quickly from ≈3 to ≈10 GeV (exactly from 2.7 to 7.7 GeV) and then slowly at above 10 GeV with the increase of collision energy. In particular, there is a plateau from near 10 GeV to 200 GeV in the excitation function of kinetic freeze-out temperature.

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“…We now discuss the chemical potential

of the i -th parton. Generally, the chemical potential

of a particle obviously affects the particle production at low energy [ 52 , 53 , 54 , 55 , 56 , 57 , 58 ]. For baryons (mostly protons and neutrons), the chemical potential

related to collision energy

is empirically given by

where both

and

are in the units of GeV [ 59 , 60 , 61 ].…”

Section: Formalism and Methodsmentioning

confidence: 99%

Excitation Functions of Tsallis-Like Parameters in High-Energy Nucleus–Nucleus Collisions

Liu

Olimov

2021

Entropy

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“…Phase transitions of systems obeying modified statistics have been studied particularly for generalized q-statistics in [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], where the corresponding critical condensation temperature has also been calculated [29]. An extended study of the thermodynamic properties presented in this work and other interesting ones will be reported elsewhere.…”

Section: Discussionmentioning

confidence: 99%

“…We will follow this path in order to estimate the critical temperature where the Bose condensation occurs for a quantum system characterized by the generalized statistics depending only on the probability [12,14]. This analysis has already been considered for the quantum statistics of q-generalized entropies, and quite interesting results arise [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. This particular result will also be explored here for other generalized entropies.…”

Section: Introductionmentioning

confidence: 99%

On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases

Obregón

López

Ortega-Cruz

2018

Entropy

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We explore some important consequences of the quantum ideal Bose gas, the properties of which are described by a non-extensive entropy. We consider in particular two entropies that depend only on the probability. These entropies are defined in the framework of superstatistics, and in this context, such entropies arise when a system is exposed to non-equilibrium conditions, whose general effects can be described by a generalized Boltzmann factor and correspondingly by a generalized probability distribution defining a different statistics. We generalize the usual statistics to their quantum counterparts, and we will focus on the properties of the corresponding generalized quantum ideal Bose gas. The most important consequence of the generalized Bose gas is that the critical temperature predicted for the condensation changes in comparison with the usual quantum Bose gas. Conceptual differences arise when comparing our results with the ones previously reported regarding the q-generalized Bose–Einstein condensation. As the entropies analyzed here only depend on the probability, our results cannot be adjusted by any parameter. Even though these results are close to those of non-extensive statistical mechanics for q ∼ 1 , they differ and cannot be matched for any q.

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“…Therefore, the power-like distribution like the Tsallis distribution may change the values related to the chiral symmetry: the condensate and the masses. The phase transition of chiral symmetry is an attractive topic in the Tsallis nonextensive statistics [30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator

Ishihara

2019

Int. J. Mod. Phys. E

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We studied chiral phase transition in the linear sigma model within the Tsallis nonextensive statistics in the case of small deviation from the Boltzmann-Gibbs (BG) statistics. The statistics has two parameters: the temperature T and the entropic parameter q. The normalized q-expectation value and the physical temperature T ph were employed in this study. The normalized q-expectation value was expanded as a series of the value (1 − q), where the absolute value |1 − q| is the measure of the deviation from the BG statistics. We applied the Hartree factorization and the free particle approximation, and obtained the equations for the condensate, the sigma mass, and the pion mass. The physical temperature dependences of these quantities were obtained numerically. We found following facts. The condensate at q is smaller than that at q ′ for q > q ′ . The sigma mass at q is lighter than that at q ′ for q > q ′ at low physical temperature, and the sigma mass at q is heavier than that at q ′ for q > q ′ at high physical temperature. The pion mass at q is heavier than that at q ′ for q > q ′ . The difference between the pion masses at different values of q is small for T ph ≤ 200 MeV. That is to say, the condensate and the sigma mass are affected by the Tsallis nonextensive statistics of small |1 − q|, and the pion mass is also affected by the statistics of small |1 − q| except for T ph ≤ 200 MeV.

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Chiral Phase Transition in Linear Sigma Model with Nonextensive Statistical Mechanics

Cited by 16 publications

References 29 publications

Excitation Functions of Tsallis-Like Parameters in High-Energy Nucleus–Nucleus Collisions

Excitation Functions of Tsallis-Like Parameters in High-Energy Nucleus–Nucleus Collisions

On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases

Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator

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