Classical and Quantum Dynamics in an Information Theoretic Space

Quantum Physics [Submitted on 9 Apr 2026] Classical and Quantum Dynamics in an Information Theoretic Space Sean Golder, Christopher Griffin We study elementary classical and quantum dynamics in an information geometric space corresponding to a Bernoulli random variable, extending work by Goehle and Griffin [Chaos, Solitons & Fractals, 188, 115535, (2024)], who study the information theoretic analog of the spring-mass system. Information geometric constructions are useful in both statistical physics and in physical interpretations of Friston's free energy principle, a form of the Bayesian brain hypothesis. In this letter, we derive the spectrum for the Laplace-Beltrami operator in Bernoulli space and find Green's functions for the Helmholtz equation, which provides solutions to the wave, heat, and Poisson equations. We then show how to quantize momentum in Bernoulli space and obtain energies and wavefunctions for both a free particle and a variety of quantum (harmonic) oscillators in this space. In particular, we show that quadratic approximation of the Kullback-Leibler potential used by Goehle and Griffin results in a quantum oscillator in information space that is equivalent to a quantum pendulum in Euclidean space. Comments: 10 pages, 3 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.09735 [quant-ph]   (or arXiv:2604.09735v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.09735 Focus to learn more Submission history From: Christopher Griffin [view email] [v1] Thu, 9 Apr 2026 19:09:36 UTC (280 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)