Dynamical Approach to Temperature

We present a new dynamical approach for measuring the temperature of a Hamiltonian dynamical systems in the microcanonical ensemble of thermodynamics. We show that under the hypothesis of ergodicity the temperature can be computed as a time average of the functional, $▽̇(▽H/\Vert ▽H{\Vert }^2)$, 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.