Hamilton-Jacobi Formalism for Thermodynamics


Cuidado, post para físicos!!! Acaba de sair no arXiv um e-print muuuuito interessante. O autor se propõe a descrever a termodinâmica com o formalismo de Hamilton-Jacobi, aquele usado em mecânica clássica e quântica (vide Nivaldo Lemos e Sakurai, respectivamente). Vejam o abstract:

“We 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 \m{n} thermodynamic degrees of freedom it is \m{2n+1}-dimensional. The equations of state of a substance pick out an \m{n}-dimensional submanifold. A family of substances whose equations of state depend on \m{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.”
Link para o artigo completo:

http://arxiv.org/abs/0711.4319

 

That’s all for now!!!

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