Thermodynamics for Trajectories of a Mass Point

TL;DR

This paper introduces a thermodynamic framework for classical particle trajectories using information theory, unifying classical and quantum mechanics through a statistical mechanical approach based on maximum entropy.

Contribution

It proposes a novel formalism that treats particle trajectories as dynamical variables within a geometric and statistical mechanics framework, linking classical and quantum mechanics.

Findings

Classical mechanics is interpreted as an equilibrium state of a trajectory-based statistical mechanics.

A partition function for trajectories is constructed, enabling thermodynamic analysis.

The maximum entropy principle unifies classical and quantum mechanics perspectives.

Abstract

On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated geometrically as dynamical variables. Statistical mechanics of particle trajectories are constructed in a classical manner. Thermodynamic variables are introduced through a partition function based on a canonical ensemble of trajectories. Within this theoretical framework, classical mechanics can be interpreted as an equilibrium state of statistical mechanics. The relationships between classical and quantum mechanics are discussed from this statistical mechanical viewpoint. The maximum entropy principle is shown to provide a unified view of both classical and quantum mechanics.