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.
Highlights
Quantum mechanics is considered to be the most basic theory of nature
The microscopic details of statistical mechanics were replaced by quantum mechanics instead of by classical mechanics, the consequences of thermal dynamics remain true, and again thermal dynamics plays the role of a guiding principle in constructing a theory
We propose to construct the thermodynamics of quantum mechanics and pursue the underlying mechanics, which must be a more fundamental theory of nature
Summary
Quantum mechanics is considered to be the most basic theory of nature. All phenomena, including gravitational interactions, have an underlying quantum-mechanical interpretation. Understanding why and how the probabilistic nature of quantum mechanics emerges from a primary principle is of critical importance To pursue this purpose, we propose to use a thermodynamic theory. Statistical mechanics was constructed on the basis of the microscopic details of classical mechanics using thermodynamics as a guiding principle. The microscopic details of statistical mechanics were replaced by quantum mechanics instead of by classical mechanics, the consequences of thermal dynamics remain true, and again thermal dynamics plays the role of a guiding principle in constructing a theory. We attempt to construct the thermodynamics of classical and quantum mechanics of a mass point. To construct the thermodynamics of classical mechanics, an appropriate definition of entropy must be introduced. The M becomes a Riemannian manifold with an indefinite metric
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