A Hamilton-Jacobi Formalism for Thermodynamics

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dc.creatorRajeev, S. G.
dc.date2007-11-27
dc.date2007-12-04
dc.date.accessioned2026-07-07T11:54:24Z
dc.date.available2026-07-07T11:54:24Z
dc.descriptionWe show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with n thermodynamic degrees of freedom it is (2n+1)-dimensional. The equations of state of a substance pick out an n-dimensional submanifold. A family of substances whose equations of state depend on n parameters define a hypersurface of co-dimension one. This can be described by the vanishing of a function which plays the role of a Hamiltonian. The ordinary differential equations (characteristic equations) defined by this function describe a dynamical system on the hypersurface. Its orbits can be used to reconstruct the equations of state. The `time' variable associated to this dynamics is related to, but is not identical to, entropy. After developing this formalism on well-grounded systems such as the van der Waals gases and the Curie-Weiss magnets, we derive a Hamilton-Jacobi equation for black hole thermodynamics in General Relativity. The cosmological constant appears as a constant of integration in this picture.
dc.descriptionMinor typos fixed
dc.identifierhttps://arxiv.org/abs/0711.4319
dc.identifierhttp://arxiv.org/abs/0711.4319
dc.identifierAnnalsPhys.323:2265-2285,2008
dc.identifierdoi:10.1016/j.aop.2007.12.007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/204889
dc.subjectHigh Energy Physics - Theory
dc.subjectStatistical Mechanics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.subjectDynamical Systems
dc.titleA Hamilton-Jacobi Formalism for Thermodynamics
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