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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 p 0 behaves as a gauge factor. When regarded as independent, the variables q i , p i (i = 0, ..., n) define a space T having a canonical symplectic structure where they appear as conjugate. A thermodynamic system is represented by a n + 1-dimensional gauge-invariant Lagrangean submanifold M of T. Any thermodynamic process, even dissipative, taking place on M is represented by a Hamiltonian trajectory in T, governed by a Hamiltonian function which is zero on M. A mapping between the equations of state of different systems is likewise represented by a canonical transformation in T. 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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The solution of the set of partial differential equations that determines the shape of the elution profile of a finite concentration band in gas chromatography is discussed. It is shown that for the simple case of the elution of a one-component band, in the approximation of the nonlinear, ideal problem, the use of a Godounov scheme permits the design of a computer program which gives an excellent approximation of the elution band profile. In the case of a strong isothermal effect, with «-hexane adsorbed on graphitized thermal carbon black, the comparison between the calculated results and those obtained experimentally shows excellent agreement. At present the most significant source of discrepancy between experimental and predicted profiles is the experimental errors made in the determination of the equilibrium isotherm of the studied compound between mobile and stationary phase, and especially in the determination of the curvature of this isotherm at the origin.

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