Classical and Quantum Dynamics in an Information Theoretic Space
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Quantum Physics arXiv:2604.09735 (quant-ph) [Submitted on 9 Apr 2026] Title:Classical and Quantum Dynamics in an Information Theoretic Space Authors:Sean Golder, Christopher Griffin View a PDF of the paper titled Classical and Quantum Dynamics in an Information Theoretic Space, by Sean Golder and Christopher Griffin View PDF HTML (experimental) Abstract: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: 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 arXiv-issued DOI via DataCite (pending registration) Submission history From: Christopher Griffin [view email] [v1] Thu, 9 Apr 2026 19:09:36 UTC (280 KB) Full-text links: Access Paper: View a PDF of the paper titled Classical and Quantum Dynamics in an Information Theoretic Space, by Sean Golder and Christopher GriffinView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)