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Hamiltonian structure of thermodynamics with gauge
The state of a thermodynamic system being characterized by its set of
extensive variables we write the associated intensive
variables the partial derivatives of the entropy in the form where
behaves as a gauge factor. When regarded as independent, the variables
define a space having a canonical
symplectic structure where they appear as conjugate. A thermodynamic system is
represented by a -dimensional gauge-invariant Lagrangian submanifold
of Any thermodynamic process, even dissipative,
taking place on is represented by a Hamiltonian trajectory in
governed by a Hamiltonian function which is zero on
A mapping between the equations of state of different systems is likewise
represented by a canonical transformation in Moreover a natural
Riemannian metric exists for any physical system, with the 's as
contravariant variables, the 's as covariant ones. Illustrative examples
are given.Comment: Proofs corrections latex vali.tex, 1 file, 28 pages [SPhT-T00/099],
submitted to Eur. Phys. J.