Epistemic uncertainty from an averaged Hamilton-Jacobi formalism

TL;DR

This paper introduces an extension of classical statistical mechanics to derive quantum-like epistemic uncertainty using an averaged Hamilton-Jacobi formalism, connecting classical and quantum frameworks.

Contribution

It presents a novel derivation of quantum dynamics assumptions from classical statistical mechanics principles, bridging the gap between classical and quantum theories.

Findings

Derivation of quantum assumptions from classical mechanics

Introduction of an averaged Hamilton-Jacobi formalism

Connection between classical and quantum uncertainties

Abstract

In recent years, the non-relativistic quantum dynamics derived from three assumptions; i) probability current conservation, ii) average energy conservation, and iii) an epistemic momentum uncertainty [A. Budiyono and D. Rohrlich, \href{https://doi.org/10.1038/s41467-017-01375-w}{Nat. Commun 8, 1306 (2017)}]. Here we show that, these assumptions can be derived from a natural extension of classical statistical mechanics.