Towards a mathematical theory of the Madelung equations: Takabayasi's quantization condition, quantum quasi-irrotationality, weak formulations, and the Wallstrom …

M Reddiger, B Poirier - Journal of Physics A: Mathematical and …, 2023 - iopscience.iop.org
Even though the Madelung equations are central to many'classical'approaches to the
foundations of quantum mechanics such as Bohmian and stochastic mechanics, no …

Governing without a fundamental direction of time: Minimal primitivism about laws of nature

EK Chen, S Goldstein - Rethinking the Concept of Law of Nature: Natural …, 2022 - Springer
Abstract The Great Divide in metaphysical debates about laws of nature is between
Humeans, who think that laws merely describe the distribution of matter, and non-Humeans …

The unexpected resurgence of Weyl geometry in late 20th-century physics

E Scholz - Beyond Einstein: Perspectives on geometry, gravitation …, 2018 - Springer
Weyl's original scale geometry of 1918 (“purely infinitesimal geometry”) was withdrawn by its
author from physical theorizing in the early 1920s. It made a surprising comeback, however …

Koopman analysis of quantum systems

S Klus, F Nüske, S Peitz - Journal of Physics A: Mathematical and …, 2022 - iopscience.iop.org
Koopman operator theory has been successfully applied to problems from various research
areas such as fluid dynamics, molecular dynamics, climate science, engineering, and …

Entropy-a guide for the perplexed

R Frigg, C Werndl - 2011 - philpapers.org
Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines
ranging from logic and statistics to biology and economics. However, a closer look reveals a …

Derivation of Dirac equation from the stochastic optimal control principles of quantum mechanics

V Yordanov - Scientific Reports, 2024 - nature.com
In this paper, we present a stochastic approach to relativistic quantum mechanics. We
formulate the three fundamental principles of this theory and derive the Dirac equations …

A discrete Schrödinger equation via optimal transport on graphs

SN Chow, W Li, H Zhou - Journal of Functional Analysis, 2019 - Elsevier
Abstract In 1966, Edward Nelson presented an interesting derivation of the Schrödinger
equation using Brownian motion. Recently, this derivation is linked to the theory of optimal …

Bild Conception of Scientific Theory Structuring in Classical and Quantum Physics: From Hertz and Boltzmann to Schrödinger and De Broglie

A Khrennikov - Entropy, 2023 - mdpi.com
We start with a methodological analysis of the notion of scientific theory and its interrelation
with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and …

Stochastic emergent quantum gravity

J Erlich - Classical and Quantum Gravity, 2018 - iopscience.iop.org
We present a stochastic framework for emergent quantum gravity coupled to matter. The
Hamiltonian constraint in diffeomorphism-invariant theories demands the identification of a …

Bouncing oil droplets, de Broglie's quantum thermostat, and convergence to equilibrium

M Hatifi, R Willox, S Colin, T Durt - Entropy, 2018 - mdpi.com
Recently, the properties of bouncing oil droplets, also known as “walkers,” have attracted
much attention because they are thought to offer a gateway to a better understanding of …