Probabilistic whereabouts of the "quantum potential"

TL;DR

This paper reviews how the functional expression involving the Laplacian of the square root of density appears in diffusion processes and quantum dynamics, focusing on pressure terms and their interpretations.

Contribution

It provides a comprehensive review of the roles and interpretations of the quantum potential-like expression across diffusion and quantum dynamical theories.

Findings

Identification of the expression in various physical contexts

Analysis of pressure term manifestations

Clarification of the expression's physical meaning

Abstract

We review major appearances of the functional expression $\pm \Delta \rho ^{1/2}/ \rho ^{1/2}$ in the theory of diffusion-type processes and in quantum mechanically supported dynamical scenarios. Attention is paid to various manifestations of "pressure" terms and their meaning(s) in-there.