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Bibliographic Details
Main Authors: Preston, Serge, Vargo, James
Format: Preprint
Published: 2005
Subjects:
Online Access:https://arxiv.org/abs/math/0509267
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Table of Contents:
  • We study the indefinite metric $G$ in the contact phase space $(P,θ)$ of a homogeneous thermodynamical system introduced by R. Mrugala. We calculate the curvature tensor, Killing vector fields, second fundamental form of Legendre submanifolds of $P$ - constitutive surfaces of different homogeneous thermodynamical systems. We established an isomorphism of the space $(P,θ,G)$ with the Heisenberg Lie group $H_{n}$ endowed with the right invariant contact structure and the right invariant indefinite metric. The lift $\tG$ of the metric $G$ to the symplectization $\tP$ of contact space $(P,θ)$, its curvature properties, and its Killing vector fields are studied. Finally we introduce the "hyperbolic projectivization" of the space $(\tP,{\tilde θ}, \tG)$ that can be considered as the natural {\bf compactification} of the thermodynamical phase space $(P,θ, G).$