Dynamical approach to the microcanonical ensemble

An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to traditional Ensemble methods. Thermodynamic properties are extracted from effective motion equations. These equations are obtained by introducing a general variational principle applied to an action averaged over a statistical ensemble of paths defined on the constant energy surface. The method is applied first to the one dimensional (\beta)-FPU chain and to the two dimensional lattice (\phi ^{4}) model. In both cases the method gives a good insight of some of their statistical and dynamical properties.