dorsal/arxiv
View SchemaGeometrothermodynamics
| Authors | Hernando Quevedo |
|---|---|
| Categories | |
| ArXiv ID | physics/0604164 |
| URL | https://arxiv.org/abs/physics/0604164 |
| DOI | 10.1063/1.2409524 |
| Journal | J.Math.Phys. 48 (2007) 013506 |
Abstract
We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the thermodynamic phase space and, on the other hand, on the metric structure of the space of thermodynamic equilibrium states. In order to make these two structures compatible we introduce a Legendre invariant set of metrics in the phase space, and demand that their pullback generates metrics on the space of equilibrium states. We show that Weinhold's metric, which was introduced {\it ad hoc}, is not contained within this invariant set. We propose alternative metrics which allow us to redefine the concept of thermodynamic length in an invariant manner and to study phase transitions in terms of curvature singularities.
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"abstract": "We present the fundamentals of geometrothermodynamics, an approach to study\nthe properties of thermodynamic systems in terms of differential geometric\nconcepts. It is based, on the one hand, upon the well-known contact structure\nof the thermodynamic phase space and, on the other hand, on the metric\nstructure of the space of thermodynamic equilibrium states. In order to make\nthese two structures compatible we introduce a Legendre invariant set of\nmetrics in the phase space, and demand that their pullback generates metrics on\nthe space of equilibrium states. We show that Weinhold\u0027s metric, which was\nintroduced {\\it ad hoc}, is not contained within this invariant set. We propose\nalternative metrics which allow us to redefine the concept of thermodynamic\nlength in an invariant manner and to study phase transitions in terms of\ncurvature singularities.",
"arxiv_id": "physics/0604164",
"authors": [
"Hernando Quevedo"
],
"categories": [
"physics.chem-ph",
"gr-qc",
"math-ph",
"math.MP"
],
"doi": "10.1063/1.2409524",
"journal_ref": "J.Math.Phys. 48 (2007) 013506",
"title": "Geometrothermodynamics",
"url": "https://arxiv.org/abs/physics/0604164"
},
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