Non-Markovian and Thermodynamic Signatures in the Classicality Assessment via Kolmogorov Consistency

Quantum Physics arXiv:2601.01122 (quant-ph) [Submitted on 3 Jan 2026] Title:Non-Markovian and Thermodynamic Signatures in the Classicality Assessment via Kolmogorov Consistency Authors:Arghya Maity, Ahana Ghoshal, Kelvin Onggadinata, Teck Seng Koh View a PDF of the paper titled Non-Markovian and Thermodynamic Signatures in the Classicality Assessment via Kolmogorov Consistency, by Arghya Maity and 3 other authors View PDF HTML (experimental) Abstract:The Kolmogorov consistency condition (KCC) defines the statistical boundary between classical and quantum dynamics. Its violation signifies the breakdown of a classical Markov description of temporal correlations. In this work, we establish a direct analytical connection between KCC violation and non-Markovianity in open quantum dynamics, revealing how memory effects manifest as departures from classical probabilistic consistency. Within a generic two-level open quantum system framework, we establish quantitative connections between the magnitude of KCC violation and key information-theoretic and thermodynamic quantities, such as mutual information, the Fano factor, heat exchange, and entropy production rate, thereby enabling a thermodynamic interpretation of temporal quantum correlations. Furthermore, we uncover formal correspondences between KCC violation, the Leggett-Garg inequality, and the negativity of the Kirkwood-Dirac quasi-distribution, identifying them as complementary witnesses of temporal quantum non-classicality. Our results thus provide a unified framework linking information-theoretic, thermodynamic, and temporal indicators of quantumness in open quantum systems. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.01122 [quant-ph] (or arXiv:2601.01122v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.01122 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Arghya Maity [view email] [v1] Sat, 3 Jan 2026 08:50:07 UTC (131 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-Markovian and Thermodynamic Signatures in the Classicality Assessment via Kolmogorov Consistency, by Arghya Maity and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)