Contact Riemannian geometry and thermodynamics

Hernández, Gerardo; Lacomba, Ernesto A.

doi:10.1016/s0926-2245(98)00006-0

Cited by 29 publications

(16 citation statements)

References 26 publications

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“…, 1). The set (T , , G) defines a contact Riemannian manifold [17,21] if the condition ∧ (d ) n = 0 is satisfied. Moreover, the metric G is Legendre invariant if its functional dependence on Z A does not change under a Legendre transformation [29].…”

Section: Review Of Geometrothermodynamicsmentioning

confidence: 99%

“…This implies that each system possesses its own space E. On the other hand, on T it is always possible to introduce the fundamental Gibbs 1-form which, when projected on E with the pullback of ϕ, generates the first law of thermodynamics and the conditions for thermodynamic equilibrium. Furthermore, on T it is also possible to consider Riemannian structures [20,21].…”

Section: Introductionmentioning

confidence: 99%

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Geometrothermodynamics of black holes

2008

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The thermodynamics of black holes is reformulated within the context of the recently developed formalism of geometrothermodynamics. This reformulation is shown to be invariant with respect to Legendre transformations, and to allow several equivalent representations. Legendre invariance allows us to explain a series of contradictory results known in the literature from the use of Weinhold's and Ruppeiner's thermodynamic metrics for black holes. For the Reissner-Nordstr\"om black hole the geometry of the space of equilibrium states is curved, showing a non trivial thermodynamic interaction, and the curvature contains information about critical points and phase transitions. On the contrary, for the Kerr black hole the geometry is flat and does not explain its phase transition structure.Comment: Revised version, to be published in Gen.Rel.Grav.(Mashhoon's Festschrift

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Section: Review Of Geometrothermodynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geometrothermodynamics of black holes

2008

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“…Several other cases have been investigated in [6,19,20,22], including that of transformations deforming an ideal gas into a van der Waals gas (see also [23]). For an analysis of equilibrium thermodynamics using symplectic structures and the Dirac formalism for constrained systems, see [12,24].…”

Section: Reversible Thermodynamicsmentioning

confidence: 99%

Contact Hamiltonian Dynamics: The Concept and Its Use

Bravetti

2017

Entropy

128

100

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“…Contact geometry [58,59] hasn't received much attention in physics literature until the recent years. This geometric setting is widely used to study thermodynamics [38,40,41], mechanical systems with Rayleigh dissipation [60,61] as well as statistical mechanics [62]. Contact geometry is the odd dimensional counterpart of the more familiar symplectic geometry [63].…”

Section: Introductionmentioning

confidence: 99%

Contact geometry and thermodynamics of black holes in AdS spacetimes

Ghosh

Bhamidipati

2019

Phys. Rev. D

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In this paper we discuss a formulation of extended phase space thermodynamics of black holes in Anti de Sitter (AdS) space-time, from the contact geometry point of view. Thermodynamics of black holes can be understood within the framework of contact geometry as flows of vector fields generated by Hamiltonian functions on equilibrium submanifolds in the extended phase space, that naturally incorporates the structure of a contact manifold. Deformations induced by the contact vector fields are used to construct various maps among thermodynamic quantities. Thermodynamic variables and equations of state of Schwarzschild black holes are mapped to that of Reissner-Nordstrom black holes in AdS, with charge as the deformation parameter. In addition, the equations of state of general black holes in AdS are shown to emerge from the high temperature ideal gas limit equations, via suitable deformations induced by contact vector fields. The Hamilton-Jacobi formalism analogous to mechanics is set up and the corresponding characteristic curves of contact vector fields are explicitly obtained, to model thermodynamic processes of black holes. Extension to thermodynamic cycles in this framework is also discussed.

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Contact Riemannian geometry and thermodynamics

Cited by 29 publications

References 26 publications

Geometrothermodynamics of black holes

Geometrothermodynamics of black holes

Contact Hamiltonian Dynamics: The Concept and Its Use

Contact geometry and thermodynamics of black holes in AdS spacetimes

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