A Dynamical Approach to Temperature

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We present a new dynamical approach for measuring the temperature of a Hamiltonian dynamical system in the micro canonical ensemble of thermodynamics. We show that under the hypothesis of ergodicity the temperature can be computed as a time-average of the functional, div(grad H/|grad H|²), on the energy-surface. Our method not only yields an efficient computational approach for determining the temperature it also provides an intrinsic link between dynamical systems theory and the statistical mechanics of Hamiltonian systems.