Abstract:
Denoting by q i i = 1,..., n the set of extensive variables which characterize the state of a thermodynamic system, we write the associated intensive variables γ i, the partial derivatives of the entropy S = S q 1,..., q n ≡q 0, in the form γ i = - p i/p 0 where p0 behaves as a gauge factor. When regarded as independent, the variables q i, p i i = 0,..., n define a space having a canonical symplectic structure where they appear as conjugate. A thermodynamic system is represented by a n + 1-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 Riemannian metric arises naturally from statistical mechanics for any thermodynamic system, with the differentials dq i as contravariant components of an infinitesimal shift and the dp i's as covariant ones. Illustrative examples are given.
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Received 5 July 2000 and Received in final form 2 March 2001
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Balian, R., Valentin, P. Hamiltonian structure of thermodynamics with gauge. Eur. Phys. J. B 21, 269–282 (2001). https://doi.org/10.1007/s100510170202
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DOI: https://doi.org/10.1007/s100510170202