Entropy, geometry, and the quantum potential

TL;DR

This paper explores how quantum potential naturally arises in classical equations through wave functions, linking it to entropy, Fisher information, and gravity, offering a unified view of quantum and geometric concepts.

Contribution

It demonstrates the emergence of quantum potential from classical equations using wave functions and connects entropy and Fisher information to gravity and quantum phenomena.

Findings

Quantum potential emerges naturally in classical equations with wave functions

Fisher information and entropy relate quantum potential to momentum fluctuations

Connections between entropy, Einstein equations, and quantum mechanics are reviewed

Abstract

We sketch and emphasize the automatic emergence of a quantum potential Q in e.g. classical WDW type equations upon inserting a (Bohmian) complex wave function. The interpretation of Q in terms of momentum fluctuations via Fisher information and entropy ideas is discussed along with the essentially forced role of the amplitude squared as a probability density. We also review the constructions of Padmanabhan connecting entropy and the Einstein equations.