Geometrothermodynamics: Comments, critics, and supports

Abstract

We write explicitly the Euler identity and the Gibbs-Duhem relation for thermodynamic potentials that are not homogeneous first-order functions of their natural extensive variables. We apply the rules to the theory of geometrothermodynamics and show how the use of the natural extensive variables, instead of the modified ones, leads to misleading results. We further reveal some other ambiguities and inconsistencies in the theory and we make new suggestions.

7 pages, no figures, more extended version: new equations added (European Physical Journal C)

References in corpus (6)

• Geometrothermodynamics of black holes
• Hawking radiation in a $d$-dimensional static spherically-symmetric black Hole surrounded by quintessence
• Phase transitions in geometrothermodynamics
• Killing Symmetries and Smarr Formula for Black Holes in Arbitrary Dimensions
• Thermodynamics of a class of non-asymptotically flat black holes in Einstein-Maxwell-Dilaton theory
• On `The conformal metric structure of Geometrothermodynamics': Generalizations

Cited by in corpus (12)

• Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry
• Black hole thermodynamics: No inconsistency via the inclusion of the missing P-V terms
• Extrinsic and intrinsic curvatures in thermodynamic geometry
• Geometrothermodynamics as a singular conformal thermodynamic geometry
• Geometrothermodynamics of black holes in Lovelock gravity with a nonlinear electrodynamics
• Einstein-Maxwell-Dilatonic phantom black holes: Thermodynamics and geometrothermodynamics
• Geometrothermodynamics of phantom AdS black holes
• Homogeneity and thermodynamic identities in geometrothermodynamics
• Analytic Electrically Charged Black Holes in $F(R)$-ModMax Theory
• Geometrothermodynamics of black holes in Lorentz non-invariant massive gravity
• Black hole horizons can hide positive heat capacity
• Rotating and non-linear magnetic-charged black hole with an anisotropic matter field