The Classical Limit of Entropic Quantum Dynamics

TL;DR

This paper derives the classical behavior of a system's center of mass within entropic quantum dynamics, showing that large systems with uncorrelated initial states follow classical trajectories as a result of a central limit theorem.

Contribution

It demonstrates how classical mechanics emerges from entropic quantum dynamics for large systems, maintaining finite Planck's constant throughout.

Findings

Center of mass follows classical Hamilton-Jacobi dynamics

Quantum potential vanishes in the classical limit

Classical trajectories emerge from entropic inference for large systems

Abstract

The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that Planck's constant remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and if the CM is initially uncorrelated with other degrees of freedom, then the CM follows a smooth trajectory and obeys the classical Hamilton-Jacobi with a vanishing quantum potential.