  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.
