Black hole entropy and the zeroth law of thermodynamics

Czinner, Viktor G.

doi:10.1142/s0218271815420158

Cited by 25 publications

(27 citation statements)

References 32 publications

(27 reference statements)

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“…These results are consistent with what we had previously found in studying the Schwarzschild solution by using the same approach [17].…”

Section: Discussionsupporting

confidence: 93%

“…Indeed, we started with the question of the nonextensivity/nonadditivity of the standard black hole entropy function, but we have not yet discussed whether it can satisfy the equilibrium compatibility condition of Abe's formula. In a recent paper [17], we investigated the thermodynamic and stability problem of a Schwarzschild black hole by considering the nonadditive entropy composition rule that is emerging from the Bekenstein-Hawking description. We showed that in this case the entropy composition rule of the Schwarzschild problem takes the form…”

Section: A Nonparametric Approachmentioning

confidence: 99%

“…The Bekenstein-Hawking black hole entropy also seems to be nonextensive because it is proportional to the area of the horizon instead of being proportional to the black hole volume (although the problem of how to compute the volume of a general black hole and how it is related to the horizon area is also a nontrivial question [6]). The nonextensive nature of black hole thermodynamics has been studied with many approaches and various methods [7][8][9][10][11][12][13][14][15][16], and in the present paper we also consider a simple model to the Kerr problem that we have already investigated in the Schwarzschild case [17]. The main idea behind this approach is to study the system in equilibrium while also requiring to satisfy the zeroth law of thermodynamics.…”

Section: Introductionmentioning

confidence: 99%

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A Zeroth Law Compatible Model to Kerr Black Hole Thermodynamics

Czinner

Iguchi

2017

Universe

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Abstract:We consider the thermodynamic and stability problem of Kerr black holes arising from the nonextensive/nonadditive nature of the Bekenstein-Hawking entropy formula. Nonadditive thermodynamics is often criticized by asserting that the zeroth law cannot be compatible with nonadditive composition rules, so in this work we follow the so-called formal logarithm method to derive an additive entropy function for Kerr black holes also satisfying the zeroth law's requirement. Starting from the most general, equilibrium compatible, nonadditive entropy composition rule of Abe, we consider the simplest non-parametric approach that is generated by the explicit nonadditive form of the Bekenstein-Hawking formula. This analysis extends our previous results on the Schwarzschild case, and shows that the zeroth law-compatible temperature function in the model is independent of the mass-energy parameter of the black hole. By applying the Poincaré turning point method, we also study the thermodynamic stability problem in the system.

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“…These results are consistent with what we had previously found in studying the Schwarzschild solution by using the same approach [17].…”

Section: Discussionsupporting

confidence: 93%

Section: A Nonparametric Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Zeroth Law Compatible Model to Kerr Black Hole Thermodynamics

Czinner

Iguchi

2017

Universe

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“…The corresponding thermodynamic and stability problems (by also applying the formal logarithm method) has been studied in [72] and [73], respectively.…”

Section: Discussionmentioning

confidence: 99%

Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

Czinner

Iguchi

2017

Eur. Phys. J. C

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Thermodynamics of rotating black holes described by the Rényi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the Rényi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a HawkingPage transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the Rényi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.

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“…. , n. As we noted before, H α and R α are optimized by the same maximum entropy distribution (27) algthough the generalized coldness β L α depends on h and is related to β L α in accordance to equation (32). Thus, ME distribution can be represented in the form…”

Section: On the Equivalence Between Four Versions Of Generalized Thermentioning

confidence: 99%

Equivalence between four versions of thermostatistics based on strongly pseudoadditive entropies

2019

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The class of strongly pseudo-additive entropies, which can be represented as an increasing continuous transformation of Shannon and Rényi entropies, have intensively been studied in previous decades. Although their mathematical structure has thoroughly been explored and established by generalized Shannon-Khinchin axioms, the analysis of their thermostatistical properties have mostly been limited to special cases which belong to two parameter Sharma-Mittal entropy class, such as Tsallis, Renyi and Gaussian entropies.In this paper we present a general analysis of the strongly pseudo-additive entropies thermostatistics by taking into account both linear and escort constraints on internal energy. We develop two types of dualities between the thermostatistics formalisms. By the first one, the formalism of Rényi entropy is transformed in the formalism of SPA entropy under general energy constraint and, by the second one, the generalized thermostatistics which corresponds to the linear constraint is transformed into the one which corresponds to the escort constraint. Thus, we establish the equivalence between four different thermostatistics formalisms based on Rényi and SPA entropies coupled with linear and escort constraints and we provide the transformation formulas. In this way we obtain a general framework which is applicable to the wide class of entropies and constraints previously discussed in the literature.As an example, we rederive maximum entropy distributions for Sharma-Mittal entropy and we establish new relationships between the corresponding thermodynamic potentials. We obtain, as special cases, previously developed expressions for maximum entropy distributions and thermodynamic quantities for Tsallis, Rényi and Gaussian entropies. In addition, the results are applied for derivation of thermostatistical relationships for supra-extensive entropy, which has not previously been considered.

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Black hole entropy and the zeroth law of thermodynamics

Cited by 25 publications

References 32 publications

A Zeroth Law Compatible Model to Kerr Black Hole Thermodynamics

A Zeroth Law Compatible Model to Kerr Black Hole Thermodynamics

Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

Equivalence between four versions of thermostatistics based on strongly pseudoadditive entropies

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