Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry

Mansoori, Seyed Ali Hosseini; Mirza, Behrouz; Fazel, Mohamadreza

doi:10.1007/jhep04(2015)115

Cited by 59 publications

(33 citation statements)

References 33 publications

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“…The first one is given by Hendi, Shahram, Panahiyan, Panah and Momennia (HPEM) in [31], where the authors consider thermodynamic metric with specific conformal function, which seems to resolve the problem of redundant singularities in Quevedo's approach. The second one is considered by Mirza and Mansoori (MM) in [32][33][34][35], which is based on conjugate thermodynamic potentials, specifically chosen to reflect the relevant thermodynamic properties of system under consideration. Some applications of these approaches to different gravitational systems can be found for example in [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic stability of the stationary Lifshitz black hole of new massive gravity

2019

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In this paper we investigate the thermodynamic properties of the stationary Lifshitz black hole solution of New Massive Gravity. We study the thermodynamic stability from local and global point of view. We also consider the space of equilibrium states for the solution within the framework of Thermodynamic Information Geometry. By investigating the proper thermodynamic metrics and their curvature invariants we find a set of restrictions on the parameter space and the critical points indicating phase transitions of the system. We confirm our findings by analytical analysis of the geodesics on the space of equilibrium states.

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Section: Introductionmentioning

confidence: 99%

Thermodynamic stability of the stationary Lifshitz black hole of new massive gravity

2019

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“…In this paper, we want to study the thermal stability and phase transition in the context of the methods of GT and extended phase space for black holes in Einstein gravity with the PMI source in higher dimensions. It is notable that, in recent years, phase transition, curvatures, Hessian matrix, and Nambu brackets have been studied via a new GT method [87][88][89][90] which, here, we are not interested in.…”

Section: Introductionmentioning

confidence: 99%

Geometrical thermodynamics and P–V criticality of the black holes with power-law Maxwell field

et al. 2017

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We study the thermodynamical structure of Einstein black holes in the presence of power Maxwell invariant nonlinear electrodynamics for two different cases. The behavior of temperature and conditions regarding the stability of these black holes are investigated. Since the language of geometry is an effective method in general relativity, we concentrate on the geometrical thermodynamics to build a phase space for studying thermodynamical properties of these black holes. In addition, taking into account the denominator of the heat capacity, we use the proportionality between cosmological constant and thermodynamical pressure to extract the critical values for these black holes. Besides, the effects of the variation of different parameters on the thermodynamical structure of these black holes are investigated. Furthermore, some thermodynamical properties such as the volume expansion coefficient, speed of sound, and isothermal compressibility coefficient are calculated and some remarks regarding these quantities are given.

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“…Some studies also show that the scalar curvature does not diverge at the singular points of the heat capacity. In order to solve this problem, some other geometries were proposed; see [25][26][27][28][29][30][31][32][33] and references therein.…”

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confidence: 99%

Ruppeiner geometry, phase transitions, and the microstructure of charged AdS black holes

Wei¹,

Liu²,

Mann³

2019

Phys. Rev. D

121

113

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We present a novel approach for probing the microstructure of a thermodynamic system that combines thermodynamic phase transitions with the Ruppeiner scalar curvature. Originally considered for van der Waals fluids and charged black holes [Phys. Rev. Lett. 123, 071103 (2019)], we extend and generalize our approach to higher-dimensional charged AdS black holes. Beginning with thermodynamic fluctuations, we construct the line element of the Ruppeiner geometry and obtain a universal formula for the scalar curvature R. We first review the thermodynamics of a van der Waals fluid and calculate the coexistence and spinodal curves. From this we are able to clearly display the phase diagram. Notwithstanding the invalidity of the equation of state in the coexistence phase regions, we find that the scalar curvature is always negative for the van der Waals fluid, indicating that attractive interactions dominate amongst the fluid microstructures. Along the coexistence curve, the scalar curvature R decreases with temperature, and goes to negative infinity at a critical temperature. We then numerically study the critical phenomena associated with the scalar curvature, and find that the critical exponent is 2, and that R(1 −T ) 2 C v ≈ 1/8, whereT and C v are the respective reduced temperature and heat capacity. We next consider four-dimensional charged AdS black holes. Vanishing of the heat capacity at constant volume yields a divergent scalar curvature. In order to extract the corresponding information, we define a new scalar curvature that has behaviour similar to that of a van der Waals fluid. We analytically confirm that at the critical point of the small/large black hole phase transition, the scalar curvature has a critical exponent 2, and R(1 −T ) 2 C v = 1/8, the same as that of a van der Waals fluid. However we also find a significant distinction: the scalar curvature can be positive for the small charged AdS black hole, implying that repulsive interactions dominate among the black hole microstructures. We then generalize our study to higher-dimensional charged AdS black holes, and investigate the influence of the dimensionality on the black hole microstructures and the scalar curvature. Our novel approach provides a universal way for probing the microstructure of charged AdS black holes from a geometric construction.

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Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry

Cited by 59 publications

References 33 publications

Thermodynamic stability of the stationary Lifshitz black hole of new massive gravity

Thermodynamic stability of the stationary Lifshitz black hole of new massive gravity

Geometrical thermodynamics and P–V criticality of the black holes with power-law Maxwell field

Ruppeiner geometry, phase transitions, and the microstructure of charged AdS black holes

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