The conformal metric structure of Geometrothermodynamics

We present a thorough analysis on the invariance of the most widely used metrics in the Geometrothermodynamics programme. We centre our attention in the invariance of the curvature of the space of equilibrium states under a change of fundamental representation. Assuming that the systems under consid...

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Bibliographic Details
Published in:Journal of mathematical physics 2013-03, Vol.54 (3), p.1
Main Authors: Bravetti, Alessandro, Lopez-Monsalvo, Cesar S., Nettel, Francisco, Quevedo, Hernando
Format: Article
Language:English
Subjects:
Curvature
Degrees of freedom
Functions (mathematics)
Geometry
Integral transforms
Invariance
Invariants
Mathematical analysis
Mathematical functions
Representations
Thermodynamics
Transformations
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Summary:We present a thorough analysis on the invariance of the most widely used metrics in the Geometrothermodynamics programme. We centre our attention in the invariance of the curvature of the space of equilibrium states under a change of fundamental representation. Assuming that the systems under consideration can be described by a fundamental relation which is a homogeneous function of a definite order, we demonstrate that such invariance is only compatible with total Legendre transformations in the present form of the programme. We give the explicit form of a metric which is invariant under total Legendre transformations and whose induced metric produces a curvature which is independent of the fundamental representation. Finally, we study a generic system with two degrees of freedom and whose fundamental relation is homogeneous of order one.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4795136