Quevedo, Hernando Geometrothermodynamics. (English) Zbl 1121.80011 J. Math. Phys. 48, No. 1, 013506, 14 p. (2007). Summary: 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, on 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 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. Cited in 2 ReviewsCited in 83 Documents MSC: 80A99 Thermodynamics and heat transfer 53C80 Applications of global differential geometry to the sciences PDFBibTeX XMLCite \textit{H. Quevedo}, J. Math. Phys. 48, No. 1, 013506, 14 p. (2007; Zbl 1121.80011) Full Text: DOI arXiv References: [1] Gibbs J., Thermodynamics 1 (1948) · Zbl 0031.13504 [2] Charatheodory C., Gesammelte Mathematische Werke 2 (1995) [3] Hermann R., Geometry, Physics and Systems (1973) [4] DOI: 10.1016/0034-4877(78)90010-1 [5] DOI: 10.1016/0034-4877(85)90059-X · Zbl 0601.58004 [6] DOI: 10.1063/1.433136 [7] DOI: 10.1063/1.433136 [8] DOI: 10.1063/1.433136 [9] DOI: 10.1063/1.433136 [10] DOI: 10.1063/1.433136 [11] DOI: 10.1063/1.449666 [12] DOI: 10.1063/1.442019 [13] DOI: 10.1063/1.440217 [14] DOI: 10.1063/1.446467 [15] DOI: 10.1063/1.448337 [16] DOI: 10.1063/1.525629 [17] DOI: 10.1103/PhysRevA.31.2520 [18] DOI: 10.1063/1.1774156 [19] DOI: 10.1016/j.chemphys.2004.10.042 [20] DOI: 10.1016/j.chemphys.2005.01.025 [21] DOI: 10.1103/PhysRevA.20.1608 [22] Torres del Castillo G. F., Rev. Mex. Fis. 39 pp 194– (1993) [23] DOI: 10.1016/S0926-2245(98)00006-0 · Zbl 0947.53040 [24] DOI: 10.1103/RevModPhys.68.313 [25] DOI: 10.1103/RevModPhys.68.313 [26] Johnston D. A., Acta Phys. Pol. B 34 pp 4923– (2003) [27] DOI: 10.1016/j.physa.2004.01.023 [28] DOI: 10.1103/PhysRevA.41.3156 [29] Quevedo H., Rev. Mex. Fis. 49 pp 125– (2003) [30] Callen H. B., Thermodynamics and an Introduction to Thermostatics (1985) · Zbl 0989.80500 [31] Arnold V. I., Mathematical Methods of Classical Mechanics (1980) [32] Burke W. L., Applied Differential Geometry (1987) [33] Israel R. B., Convexity in the Theory of Lattice Gases (1979) · Zbl 0399.46055 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.