Thermodynamic stability criterion and fluctuation theory in nonextensive thermodynamics

Zheng, Yong; Du, Jiulin; Liang, Faku

doi:10.1007/s00161-018-0628-8

Cited by 8 publications

(8 citation statements)

References 40 publications

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“…The original form of the Tsallis entropy [1] behaves as the quantum summation of the power law of the distribution probability at a given quantum state of the composite system. Due to the power-law properties, the Tsallis entropy becomes nonextensive and nonadditive, further leading to the nonadditivity of many quantities, such as the physical internal energy [32,33] and Gibbs free energy. In the microcanonical ensemble, all the microstates have the same probability, so the corresponding Tsallis entropy should adopt the form with equal probability.…”

Section: Statistical Ensemble Theory In Nsmmentioning

confidence: 99%

Theoretical self-consistency in nonextensive statistical mechanics with parameter transformation

Zheng¹,

Du²

2021

Commun. Theor. Phys.

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Self-consistency in nonextensive statistical mechanics is studied as a recourse to parameter transformation, where different nonextensive parameters are presented for various theoretical branches. The unification between the first and third choices of the average definition and that between the normal and escort distributions are both examined. The problem of parameter inversion in the generalized H theorem is also investigated. The inconsistency between the statistical ensemble pressure and molecular dynamics pressure can be eliminated. This work also verifies the equivalence of physical temperature and gravitational temperature in nonextensive statistical mechanics. In these parameter transformations, the Tsallis entropy form is observed to remain invariant.

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Section: Statistical Ensemble Theory In Nsmmentioning

confidence: 99%

Theoretical self-consistency in nonextensive statistical mechanics with parameter transformation

Zheng¹,

Du²

2021

Commun. Theor. Phys.

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“…where β ′ is the generalized Lagrange multiplier [39], "i " and "j " represent different quantum states. The cross term in (3) is derived from the interactions between different parts or states inside the system.…”

Section: The Nonextensive Grand Canonical Distribution Based On the Ementioning

confidence: 99%

“…Considering the balance conditions [39], we introduce the following generalized multipliers, , r r qr q qr q c c c c…”

Section: The Nonextensive Grand Canonical Distribution Based On the E...mentioning

confidence: 99%

“…This definition approach is of the third choice of internal energy definition [40], from which one can find that the particle number and internal energy are both additive. This energy is called Lagrange internal energy [39,41]. Similarly, the particle number is called the Lagrange particle number.…”

Section: The Nonextensive Grand Canonical Distribution Based On the E...mentioning

confidence: 99%

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Thermodynamic properties of the solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation

Zheng

2020

Eur. Phys. J. Plus

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We study the thermodynamic properties of solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation. First we study the nonextensive grand canonical distribution function and the nonextensive quantum statistics with a parameter transformation. Then we derive the generalized Boson distribution and Fermi distribution in the nonextensive quantum statistics. Further we study the thermodynamic properties of solid and metal electrons in the nonextensive quantum system, including the generalized Debye models, the generalized internal energies, the generalized capacities and chemical potential. We derive new expressions of these thermodynamic quantities, and we show that they all depend significantly on the nonextensive parameter and in the limit they recover to the forms in the classical quantum statistics. These new expressions may be applied to study the new characteristics in some nonextensive quantum systems where the long-range interactions and/or long-range correlations play a role.

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“…Apart from these two quantities, the invariable P-pressure is also the balance condition. In order to prove this, we assume [25] that the volume is also nonadditive and satisfies ( , )…”

Section: The Links Of the Nonextensive Thermodynamic Equations To The...mentioning

confidence: 99%

The dual formalisms of nonextensive thermodynamics for open systems with maximum entropy principle

Zheng¹,

Yu²,

Du³

2019

Continuum Mech. Thermodyn.

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We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the chemical potential is constant in the two sets of parallel formalisms, where the fundamental thermodynamic equations with dual interpretations of thermodynamic quantities are derived for the open systems. By introducing parallel structures of Legendre transformations, other thermodynamic equations with dual interpretations of quantities are also deduced in the open systems, and then several dual thermodynamic relations are inferred. One can easily find that there are correlations between the dual relations, from which an equivalent rule is found that the Tsallis factor is invariable in calculations of partial derivative with constant volume or constant entropy. Using this rule, more correlations can be found. And the statistical expressions of the Lagrange internal energy and pressure are easily obtained.

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Thermodynamic stability criterion and fluctuation theory in nonextensive thermodynamics

Cited by 8 publications

References 40 publications

Theoretical self-consistency in nonextensive statistical mechanics with parameter transformation

Theoretical self-consistency in nonextensive statistical mechanics with parameter transformation

Thermodynamic properties of the solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation

The dual formalisms of nonextensive thermodynamics for open systems with maximum entropy principle

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