We note that equations of state—by which we mean identical relations among the thermodynamic variables characterizing a system—are actually first‐order partial differential equations for a function which defines the thermodynamics of the system. Like the Hamilton‐Jacobi equation, such equations can be solved along trajectories given by Hamilton’s equations, the trajectories being quasistatic processes which obey the given equation of state. This gives rise to the notion of thermodynamic functions as infinitesimal generators of quasistatic processes, with a natural Poisson bracket formulation. This formulation of thermodynamic transformations is invariant under canonical coordinate transformations, just as classical mechanics is, which is to say that thermodynamics and classical mechanics have the same formal structure, namely a symplectic structure.
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Papers| June 01 1979
Mark A. Peterson; Analogy between thermodynamics and mechanics. Am. J. Phys. 1 June 1979; 47 (6): 488–490. https://doi.org/10.1119/1.11788
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