Thermodynamics: A Riemannian geometric model

Ruppeiner, George

doi:10.1103/physreva.20.1608

Cited by 710 publications

(770 citation statements)

References 14 publications

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“…There are several methods toward geometrical thermodynamics. The well known ones are: Weinhold [131,132], Ruppeiner [133,134], Quevedo [135,136] and HPEM [137,138]. Their corresponding metrics are in following forms…”

Section: Jhep05(2016)029mentioning

confidence: 99%

“…The divergencies of thermodynamical Ricci scalar may coincide to bound or phase transition points. So far, four different geometrical methods were introduced; Weinhold [131,132], Ruppeiner [133,134], Quevedo [135,136] and HPEM [137,138]. Several studies in context of black holes with consideration of such methods have been done [139][140][141][142][143][144].…”

Section: Jhep05(2016)029mentioning

confidence: 99%

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Massive charged BTZ black holes in asymptotically (a)dS spacetimes

Hendi

Panah

Panahiyan

2016

J. High Energ. Phys.

106

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Motivated by recent developments of BTZ black holes and interesting results of massive gravity, we investigate massive BTZ black holes in the presence of Maxwell and Born-Infeld (BI) electrodynamics. We study geometrical properties such as type of singularity and asymptotical behavior as well as thermodynamic structure of the solutions through canonical ensemble. We show that despite the existence of massive term, obtained solutions are asymptotically (a)dS and have a curvature singularity at the origin. Then, we regard varying cosmological constant and examine the Van der Waals like behavior of the solutions in extended phase space. In addition, we employ geometrical thermodynamic approaches and show that using Weinhold, Ruppeiner and Quevedo metrics leads to existence of ensemble dependency while HPEM metric yields consistent picture. For neutral solutions, it will be shown that generalization to massive gravity leads to the presence of non-zero temperature and heat capacity for vanishing horizon radius. Such behavior is not observed for linearly charged solutions while generalization to nonlinearly one recovers this property.

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Section: Jhep05(2016)029mentioning

confidence: 99%

Section: Jhep05(2016)029mentioning

confidence: 99%

Massive charged BTZ black holes in asymptotically (a)dS spacetimes

Hendi

Panah

Panahiyan

2016

J. High Energ. Phys.

106

View full text Add to dashboard Cite

show abstract

“…A pioneering paper on this was by Weinhold [1] who introduced a thermodynamic energy inner product. This led to the work of Ruppeiner [2] who wrote a Riemannian thermodynamic entropy metric to represent thermodynamic fluctuation theory, and was the first to systematically calculate the thermodynamic Ricci curvature scalar R. A parallel effort was by Andresen, Salamon, and Berry [3] who began the systematic application of the thermodynamic entropy metric to finite-time thermodynamic processes.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic R-diagrams reveal solid-like fluid states

Ruppeiner

Mausbach

May³

2015

Physics Letters A

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We evaluate the thermodynamic curvature R for fluid argon, hydrogen, carbon dioxide, and water. For these fluids, R is mostly negative, but we also find significant regimes of positive R, which we interpret as indicating solid-like fluid properties. Regimes of positive R are present in all four fluids at very high pressure. Water has, in addition, a narrow slab of positive R in the stable liquid phase near its triple point. Also, water is the only fluid we found having R decrease on cooling into the metastable liquid phase, consistent with a possible second critical point.Keywords: metric geometry of thermodynamics; fluid equations of state; water; thermodynamic curvature; phase transitions and critical points Extracting general information from thermodynamic properties poses a challenge. Which properties to feature depends strongly on the type of system under consideration, the regime of interest, and the broader context of applicable models from statistical mechanics. Very useful for comparison between different systems would be some representation not dependent on such subjective features. In this paper, we propose R-diagrams, based on the thermodynamic curvature R, as such a representation. At a glance, R-diagrams reveal a number of important fluid properties. We key here particularly on locating solid-like properties of fluids, with particular attention to anomalies in liquid water in the vicinity of its triple point.

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“…In 1976 Weinhold [9][10][11][12][13] proposed a metric, as the Hessian of the internal energy, given as g W ij = ∂ i ∂ j U (S, N r ). Later in 1979, Ruppeiner [14] introduced another metric as the Hessian of entropy, as g R ij = −∂ i ∂ j S (M, N r ). This Ruppeiner metric is conformally equivalent to Weinhold's metric and the geometry that can be obtained from these two methods are related through the relation where [15,16], ds 2 R = 1 T ds 2 W .…”

Section: Introductionmentioning

confidence: 99%

A unified thermodynamic picture of Hořava-Lifshitz black hole in arbitrary space time

Suresh

Tharanath

Kuriakose

2015

J. High Energ. Phys.

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Abstract:In this paper, we analyze the complete thermodynamic and phase transition phenomena of a black hole solution in Hořava-Lifshitz gravity in arbitrary space time. Nature of phase transition is studied using geometrothermodynamic and Ehrenfest's scheme of standard thermodynamics. We analytically check the Ehrenfest's equations near the critical point, which is the point of divergence in the heat capacity. Our analysis revels that this black hole exhibits a second order phase transition.

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Thermodynamics: A Riemannian geometric model

Cited by 710 publications

References 14 publications

Massive charged BTZ black holes in asymptotically (a)dS spacetimes

Massive charged BTZ black holes in asymptotically (a)dS spacetimes

Thermodynamic R-diagrams reveal solid-like fluid states

A unified thermodynamic picture of Hořava-Lifshitz black hole in arbitrary space time

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