TC/TCL and NETFD Correspondence Principles for Information Backflow: A Structural Monotonicity Theorem and Minimal Phase Diagrams
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Quantum Physics arXiv:2602.09054 (quant-ph) [Submitted on 7 Feb 2026] Title:TC/TCL and NETFD Correspondence Principles for Information Backflow: A Structural Monotonicity Theorem and Minimal Phase Diagrams Authors:Koichi Nakagawa View a PDF of the paper titled TC/TCL and NETFD Correspondence Principles for Information Backflow: A Structural Monotonicity Theorem and Minimal Phase Diagrams, by Koichi Nakagawa View PDF HTML (experimental) Abstract:We propose a unified structural framework for information backflow in minimal non-Markovian relaxation processes. The central idea is to interpret non-Markovianity as an embedding phenomenon in which observable degrees of freedom exchange information with hidden auxiliary sectors. Our approach is based on two standard formalisms in nonequilibrium physics: (i) the time-convolution (TC) and time-convolutionless (TCL) projection-operator master equations, and (ii) the correspondence principle of non-equilibrium thermo field dynamics (NETFD), which provides a doubling construction equivalent to an embedding of density-operator dynamics into a vector evolution in an enlarged space. We define a general information-backflow functional N_I associated with an information quantity I(t) and derive sufficient conditions for the absence of backflow (N_I = 0) in terms of divisibility properties of the instantaneous TCL generator. We further introduce a decomposition of backflow into classical and intrinsic thermo-field entanglement contributions, leading to a classification of transient overshoot and revival phenomena in a model-independent manner. Minimal classical and quantum two-state models are discussed as analytically tractable examples, recovering Mittag-Leffler fractional relaxation as a universal envelope. We also provide a constructive TC-to-TCL algorithm for extracting effective rates and producing phase diagrams of backflow. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2602.09054 [quant-ph] (or arXiv:2602.09054v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.09054 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Koichi Nakagawa [view email] [v1] Sat, 7 Feb 2026 09:15:54 UTC (510 KB) Full-text links: Access Paper: View a PDF of the paper titled TC/TCL and NETFD Correspondence Principles for Information Backflow: A Structural Monotonicity Theorem and Minimal Phase Diagrams, by Koichi NakagawaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cond-mat cond-mat.stat-mech 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?)