Nonextensive thermodynamic relations based on the assumption of temperature duality

Zheng, Yong; Du, Jiulin

doi:10.1007/s00161-016-0510-5

Cited by 8 publications

(17 citation statements)

References 40 publications

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“…which is different from the P-free energy expression in a closed system [20] with constant particle number. Actually, just as the traditional thermodynamics, we can further introduce the so-called grand thermodynamic potential J in each set of formalisms, that is,…”

Section: The Legendre Transformations and The Nonextensive Thermodynacontrasting

confidence: 62%

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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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Section: The Legendre Transformations and The Nonextensive Thermodynacontrasting

confidence: 62%

“…For convenience, we define q q c = i p ∑ as Tsallis factor. In the nonextensive thermodynamics, two different internal energies were proposed [20]. One is the physical internal energy (P-internal energy), defined as [21] (2) q q…”

Section: The Dual Power-law Q-distribution Functions With Maximum Entmentioning

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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“…On the other hand, either the square of energy fluctuation or particle number fluctuation, or the product of energy fluctuation and particle number fluctuation in Eq. (29), is proportional to the averaged particle number. This means that in the limit of large particle number, the cross term of Eq.…”

Section: The Nonextensive Grand Canonical Ensembles With Equiprobabilitymentioning

confidence: 99%

“…It is obvious that the grand canonical q-distribution (38) satisfies the probability independence based on the composite rule (29). Now definitions of the internal energy and the average particle number can be given by…”

Section: The Nonextensive Grand Canonical Ensembles With Equiprobabilitymentioning

confidence: 99%

“…For example, temperature can not be naturally defined in the zeroth law of thermodynamics, but it can be defined in a modified manner in fundamental thermodynamic equations of the first law. And free energy is also modified by adding the Tsalis factor [29] so that unfamiliar thermodynamic relations are produced in nonextensive thermodynamics. This is not consistent with our physical intuition, where the thermodynamic laws come from the phenomenological observations and experiments, and they are appropriate for any systems, no matter whatever statistical mechanics the systems are based on.…”

Section: Introductionmentioning

confidence: 99%

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The nonextensive statistical ensembles with dual thermodynamic interpretations

Zheng

Liu

et al. 2019

Eur. Phys. J. Plus

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The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for the limit of large particle number for most normal systems. In this case, Tsallis entropy can be expanded as a function of energy and particle number fluctuation, and thus the power-law forms of the generalized Gibbs distribution and grand canonical distribution can be derived. These new distribution functions can be applied to derive the free energy and grand thermodynamic potential in nonextensive thermodynamics. In order to establish appropriate nonextensive thermodynamic formalism, the dual thermodynamic interpretations are necessary for thermodynamic relations and thermodynamic quantities. By using a new technique of parameter transformation, the single-particle distribution can be deduced from the power-law Gibbs distribution. This technique produces a link between the statistical ensemble and the quasi-independent system with two kinds of nonextensive parameter having quite different physical explanations. Furthermore, the technique is used to construct nonextensive quantum statistics and effectively to avoid the factorization difficulty in the power-law grand canonical distribution.

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Thermodynamic stability criterion and fluctuation theory in nonextensive thermodynamics

Zheng

Liang

2018

Continuum Mech. Thermodyn.

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Nonextensive thermodynamic relations based on the assumption of temperature duality

Cited by 8 publications

References 40 publications

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

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

The nonextensive statistical ensembles with dual thermodynamic interpretations

Thermodynamic stability criterion and fluctuation theory in nonextensive thermodynamics

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