Eur. Phys. J. B 21, 269-282 (2001)
https://doi.org/10.1007/s100510170202

Hamiltonian structure of thermodynamics with gauge

¹ CEA/Saclay, Service de Physique Théorique, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
² Centre de recherches ELF, Chemin du Canal, BP 22, 69360 Solaize, France

Corresponding author: ^a balian@spht.saclay.cea.fr

Received: 5 July 2000
Revised: 2 March 2001
Published online: 15 May 2001

Abstract

Denoting by the set of extensive variables which characterize the state of a thermodynamic system, we write the associated intensive variables the partial derivatives of the entropy in the form where p₀ 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 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 as contravariant components of an infinitesimal shift and the 's as covariant ones. Illustrative examples are given.