Quantum models of classical systems

TL;DR

This paper extends quantum statistical methods to classical mechanical properties using fuzzy maximum entropy packets, aiming to unify quantum and classical models of thermodynamics and mechanics.

Contribution

It introduces fuzzy maximum entropy packets as a new approach to connect quantum and classical models, replacing sharp trajectories with more realistic, fuzzy representations.

Findings

Fuzzy models improve the match between classical and quantum trajectories.

Classical and quantum models of a stiff rod demonstrate the unified theory.

The approach bridges thermodynamic and mechanical properties in quantum-classical systems.

Abstract

Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is represented by a sharp trajectory is not testable and is replaced by a class of fuzzy models, the so-called maximum entropy (ME) packets. The fuzzier are the compared classical and quantum ME packets, the better seems to be the match between their dynamical trajectories. Classical and quantum models of a stiff rod will be constructed to illustrate the resulting unified quantum theory of thermodynamic and mechanical properties.