On the robust thermodynamical structures against arbitrary entropy form and energy mean value

Yamano, Takuya

doi:10.1007/s100510070083

Cited by 25 publications

(19 citation statements)

References 12 publications

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“…As shown in [100,101], any thermostatistical formalism constructed by following Jayne's maximum entropy prescription complies with the thermodynamical relationships. A thermodynamically consistent formulation is then obtained by the appropriate identification of the relevant constraints with the extensive thermodynamical quantities (like number of particles N or energy E) and by identification of the corresponding Lagrange multipliers with the appropriate intensive thermodynamical quantities (like temperature T and chemical potential µ).…”

Section: The Problem Of Thermodynamic Consistencymentioning

confidence: 95%

Nonextensive Nambu-Jona-Lasinio Model of QCD matter

Rożynek

Wilk

2016

Eur. Phys. J. A

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Abstract. We present a thermodynamical analysis of the nonextensive, QCD-based, Nambu-Jona-Lasinio (NJL) model of strongly interacting matter in the critical region. It is based on the nonextensive generalization of the Boltzmann-Gibbs (BG) statistical mechanics, used in the NJL model, to its nonextensive version. This can be introduced in different ways, depending on different possible choices of the form of the corresponding nonextensive entropies, which are all presented and discussed in detail. Unlike previous attempts, the present approach fulfils the basic requirements of thermodynamical consistency. The corresponding results are compared, discussed and confronted with previous findings.

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Section: The Problem Of Thermodynamic Consistencymentioning

confidence: 95%

Nonextensive Nambu-Jona-Lasinio Model of QCD matter

Rożynek

Wilk

2016

Eur. Phys. J. A

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“…This is due to the fact [10,11] that Eq. (23) holds for an arbitrary form of the entropy and an arbitrary definition of the expectation value.…”

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Generalized entropy optimized by a given arbitrary distribution

Abe

2003

J. Phys. A: Math. Gen.

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We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a basic random quantity of interest.This offers, via the maximum entropy principle, a unified basis for a great variety of distributions observed in nature, which can hardly be described by the conventional methods. As a simple example, we explicitly derive the entropy associated with the stretched exponential distribution. To include the distributions with the divergent moments (e.g., the Lévy stable distributions), it is necessary to modify the definition of the expectation value. PACS number(s): 02.50.-r, 05.20.-y, 05.90.+m, 89.20.-a

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“…DOI: 10.1103/PhysRevLett.88.020601 PACS numbers: 05.70.Ln, 05.20.Gg, 05.40. -a During the past few years there has been a great deal of interest in studying nonextensive thermodynamics [1][2][3]. This results from the assumption of nonadditive statistical entropies and the maximum statistical entropy principle, following the information theory formulation of statistical mechanics proposed by Jaynes [4].…”

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confidence: 99%

Is Tsallis Thermodynamics Nonextensive?

Vives

Planes

2001

Phys. Rev. Lett.

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Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein's formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. The use of the proposed transformation of variables also shows that fluctuations within Tsallis statistics can be mapped to those of standard statistical mechanics. DOI: 10.1103/PhysRevLett.88.020601 PACS numbers: 05.70.Ln, 05.20.Gg, 05.40. -a During the past few years there has been a great deal of interest in studying nonextensive thermodynamics [1][2][3]. This results from the assumption of nonadditive statistical entropies and the maximum statistical entropy principle, following the information theory formulation of statistical mechanics proposed by Jaynes [4]. Indeed, besides its relevance in many nonequilibrium problems, nonextensivity is of interest for systems of particles which show longrange interactions [5], as occurs in a number of ferroic materials [6] such as ferromagnetic, ferroelastic, ferroelectric solids, and astrophysical systems [7]. Within this framework, the Tsallis statistical entropy [8] has proven to be the only nonadditive generalization of Gibbs-Shannon entropy which satisfies the following properties: (i) positivity (it takes zero value for absolute certainty), increasing monotonously with increasing uncertainty, and (ii) concavity. However, many fundamental features regarding the connection between the formulation of statistical mechanics and thermodynamics remain unclear. For instance, the identification of adequate generalized thermodynamic forces and the computation of statistical fluctuations are still controversial [9]. In this Letter we clarify such problems and provide robust arguments showing the equivalence of the present formulations of nonextensive Tsallis thermodynamics with the standard extensive equilibrium formulation.Within the Tsallis formalism, the lack of information associated with any probability distribution ͕p͑i͖͒ defined on a set of microstates V ͕i͖ [10] is given bywhere the parameter q, determining the degree of nonextensivity, is positive in order to ensure the concavity of S . The q-logarithmic function is defined as ln q f ͑ f 12q 2 1͒͑͞1 2 q͒. In the q ! 1 limit, Eq. (1) reduces to the Gibbs-Shannon entropy S 2 P i p͑i͒ lnp͑i͒. In order to simplify the notation, we will indicate the set V only when necessary. The novelty of the statistical entropy (1) is that it does not satisfy additivity. Instead, for two systems A and B described by independent probability distributions,For a given physical system the equilibrium probability distribution ͕p ‫ء‬ ͑i͖͒ corresponds to the distribution that maximizes S under the normalization condition1͔ and the relevant constraints imposed by the available statistical information on the system. The thermodynamic equilibrium entr...

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On the robust thermodynamical structures against arbitrary entropy form and energy mean value

Cited by 25 publications

References 12 publications

Nonextensive Nambu-Jona-Lasinio Model of QCD matter

Nonextensive Nambu-Jona-Lasinio Model of QCD matter

Generalized entropy optimized by a given arbitrary distribution

Is Tsallis Thermodynamics Nonextensive?

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