Thermodynamics for trajectories of a mass point

On the basis of the theory of thermodynamics,a new formalism of classical nonrelativistic mechanics of amass point is proposed. The particle trajectories of a generaldynamical system defined on a (1+n)-dimensionalsmooth manifold are geometrically treated as dynamicalvariables. The statistical mechanics of particle trajectoriesare constructed in a classical manner. Thermodynamicvariables are introduced through a partition function basedon a canonical ensemble of trajectories. Within this theoreticalframework, classical mechanics can be interpretedas an equilibrium state of statistical mechanics. The relationshipbetween classical and quantum mechanics is discussedfrom the viewpoint of statistical mechanics. Themaximum-entropy principle is shown to provide a unifiedview of both classical and quantum mechanics.