Physics – Condensed Matter
Scientific paper
2000-07-18
Physics
Condensed Matter
Proofs corrections latex vali.tex, 1 file, 28 pages [SPhT-T00/099], submitted to Eur. Phys. J. B
Scientific paper
10.1007/s100510170202
The state of a thermodynamic system being characterized by its set of extensive variables $q^{i}(i=1,...,n) ,$ we write the associated intensive variables $\gamma_{i},$ the partial derivatives of the entropy $ S(q^{1},...,q^{n}) \equiv q_{0},$ in the form $\gamma_{i}=-p_{i}/p_{0}$ where $p_{0}$ behaves as a gauge factor. When regarded as independent, the variables $q^{i},p_{i}(i=0,...,n) $ define a space $\mathbb{T}$ having a canonical symplectic structure where they appear as conjugate. A thermodynamic system is represented by a $n+1$-dimensional gauge-invariant Lagrangian submanifold $\mathbb{M}$ of $\mathbb{T}.$ Any thermodynamic process, even dissipative, taking place on $\mathbb{M}$ is represented by a Hamiltonian trajectory in $\mathbb{T},$ governed by a Hamiltonian function which is zero on $\mathbb{M}.$ A mapping between the equations of state of different systems is likewise represented by a canonical transformation in $\mathbb{T}.$ Moreover a natural Riemannian metric exists for any physical system, with the $q^{i}$'s as contravariant variables, the $p_{i}$'s as covariant ones. Illustrative examples are given.
Balian Roger
Valentin P.
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