Maxwell’s equal area law for Lovelock thermodynamics

Xu, Hao; Xu, Zhen-Ming

doi:10.1142/s0218271817500377

Cited by 29 publications

(37 citation statements)

References 99 publications

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“…(3.4) is important for existence or non-existence of chaos below. This is important as the Gibbs free energy written in terms of thermodynamic volume remains unchanged during phase transition and it is the combination P dV that has the right scaling [62,63]. Following the approach in [38,43], ignoring coefficients of order O(1/v 4 ) in Taylor series expansion, the Hamiltonian can be computed to be:…”

Section: Temporal Chaos In Spinodal Regionmentioning

confidence: 99%

Chaos in charged Gauss-Bonnet AdS black holes in extended phase space

Mahish

Bhamidipati

2019

Phys. Rev. D

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We study the onset of chaos due to temporal and spatially periodic perturbations in charged Gauss-Bonnet AdS black holes in extended thermodynamic phase space, by analyzing the zeros of the appropriate Melnikov functions. Temporal perturbations coming from a thermal quench in the unstable spinodal region of P-V diagram, may lead to chaos, when a certain perturbation parameter γ saturates a critical value, involving the Gauss-Bonnet coupling α and the black hole charge Q. A general condition following from the equation of state is found, which can rule out the existence of chaos in any black hole. Using this condition, we find that the presence of charge is necessary for chaos under temporal perturbations. In particular, chaos is absent in neutral Gauss-Bonnet and Lovelock black holes in general dimensions. Chaotic behavior continues to exist under spatial perturbations, irrespective of whether the black hole carries charge or not. 1 sm19@iitbbs.ac.in 2 chandrasekhar@iitbbs.ac.in 1 arXiv:1902.08932v3 [hep-th]

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Section: Temporal Chaos In Spinodal Regionmentioning

confidence: 99%

Chaos in charged Gauss-Bonnet AdS black holes in extended phase space

Mahish

Bhamidipati

2019

Phys. Rev. D

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“…However, in our analysis we will consider an extended phase space. According to the first law of black hole thermodynamics and the interpretation of M (total mass of black hole) [21,56] as H (the black hole enthalpy) [56,57], the Gibbs free energy of the black hole can be written as…”

Section: Phase Equilibrium and Maxwell's Equal Area Lawmentioning

confidence: 99%

Q– $$\Phi $$ Φ criticality in the extended phase space of $$(n+1)$$ ( n + 1 ) -dimensional RN-AdS black holes

Zhao

Cao

2016

Eur. Phys. J. C

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In order to achieve a deeper understanding of gravity theories, i.e., the quantum properties of gravity theories and the statistical explanation of gravitational entropy, it is important to further investigate the thermodynamic properties of a black hole at the critical point, besides the phase transition and critical behaviors. In this paper, by using Maxwell's equal area law, we choose T, Q, as the state parameters and study the phase equilibrium problem of a general (n + 1)-dimensional RN-AdS black holes thermodynamic system. The boundary of the two-phase coexistence region and its isotherm and isopotential lines are presented, which may provide a theoretical foundation for studying the phase transition and phase structure of black hole systems.

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“…Thus, by making an analogy between the black hole in the AdS background and the real van der Waals fluid, we find that there also exists an oscillating part below the critical temperature T c in the P−V diagram, which indicates that the first order phase transition occurs from a small black hole to a large one. This isobar, which satisfies the Maxwell equal area law, represents the co-existence curve of small and large black holes [41]. Normally, the Maxwell equal area law is constructed in the (P, V ) plane for a constant temperature, and it can also be made in the (T, S) or ( , Q) plane.…”

Section: Maxwell Equal Area Lawmentioning

confidence: 99%

“…Based on the results pointed out above, we take advantage of the well-established Maxwell equal area law [36][37][38][39][40][41] to make a further investigation of the van der Waals-type phase transition, of the co-existence curve, and of the P−V critical phenomenon for this charged AdS hairy black hole. We give analytically the critical values of the charged hairy black hole and show in detail the behavior of the phase transition from a small black hole to a large one.…”

Section: Introductionmentioning

confidence: 99%

Validity of Maxwell equal area law for black holes conformally coupled to scalar fields in $$\text {AdS}_5$$ AdS 5 spacetime

Miao

2017

Eur. Phys. J. C

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We investigate the P−V criticality and the Maxwell equal area law for a five-dimensional spherically symmetric AdS black hole with a scalar hair in the absence of and in the presence of a Maxwell field, respectively. Especially in the charged case, we give the exact P−V critical values. More importantly, we analyze the validity and invalidity of the Maxwell equal area law for the AdS hairy black hole in the scenarios without and with charges, respectively. Within the scope of validity of the Maxwell equal area law, we point out that there exists a representative van der Waals-type oscillation in the P−V diagram. This oscillating part, which indicates the phase transition from a small black hole to a large one, can be replaced by an isobar. The small and large black holes have the same Gibbs free energy. We also give the distribution of the critical points in the parameter space both without and with charges, and we obtain for the uncharged case the fitting formula of the co-existence curve. Meanwhile, the latent heat is calculated, which gives the energy released or absorbed between the small and large black hole phases in the isothermal-isobaric procedure.

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Maxwell’s equal area law for Lovelock thermodynamics

Cited by 29 publications

References 99 publications

Chaos in charged Gauss-Bonnet AdS black holes in extended phase space

Chaos in charged Gauss-Bonnet AdS black holes in extended phase space

Q– $$\Phi $$ Φ criticality in the extended phase space of $$(n+1)$$ ( n + 1 ) -dimensional RN-AdS black holes

Validity of Maxwell equal area law for black holes conformally coupled to scalar fields in $$\text {AdS}_5$$ AdS 5 spacetime

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