Atti dell’Accademia Peloritana dei Pericolanti Classe di Scienze Fisiche, Matematiche e Naturali
Mathematical physics, Thermodynamics, Differential Geometry
We study an indefinite metric G which was introduced by R. Mrugala and is defined on the contact phase space (P, θ) of a homogeneous thermodynamical system. We describe the curvature properties and the isometry group of the metric G. We established an isomorphism of the space (P, θ, G) with the Heisenberg Lie group Hn, endowed with the right invariant contact structure and the right invariant indefinite metric. The lift of the metric G to the symplectization of contact space (P, θ) and its properties are studied. Finally we introduce the "hyperbolic projectivization" of the space () that can be considered as the natural compactification of the thermodynamical phase space (P, θ, G).
Preston, S. and Vargo, J. (2008). The Indefinite Metric of R. Mrugala and the Geometry of the Thermodynamical Phase Space. Atti della Accademia Peloritana dei Pericolanti – Classe di Scienze Fisiche, Matematiche e Naturali. Vol. LXXXVI, C1S0801019 - Suppl. 1