A Geometric, Dynamical Approach to Thermodynamics

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  • 21 March 1997
Abstract
We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. In a recent paper [Phys Rev Lett, vol 78, 772-774 (1997)] we showed that under general hypotheses the temperature defined in this ensemble is dynamically observable. Here we generalize the arguments and present simple, explicit formulas showing that also the specific heat and higher order derivatives of the entropy can be observed dynamically. Using perturbation theory we give asymptotic formulas through which the canonical ensemble, at least in principle, can be reconstructed from micro-canonical measurements only. We believe that our approach will prove useful in numerical simulations and provide a natural geometric and dynamical interpretation of the thermodynamics of classical Hamiltonian systems.

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