Phase Diagrams of Information Backflow: Unifying Entanglement Revivals and Entropy Overshoots in Minimal Non-Markovian Models

Quantum Physics arXiv:2601.18822 (quant-ph) [Submitted on 25 Jan 2026] Title:Phase Diagrams of Information Backflow: Unifying Entanglement Revivals and Entropy Overshoots in Minimal Non-Markovian Models Authors:Koichi Nakagawa View a PDF of the paper titled Phase Diagrams of Information Backflow: Unifying Entanglement Revivals and Entropy Overshoots in Minimal Non-Markovian Models, by Koichi Nakagawa View PDF HTML (experimental) Abstract:Memory effects in non-Markovian dynamics are often diagnosed either via quantum-correlation revivals or via non-monotonic classical information measures, yet a unified minimal framework comparing their ``backflow phases'' is still lacking. Here we propose an information-backflow phase-diagram approach that places \emph{quantum entanglement revivals} and \emph{classical entropy overshoots} on the same footing through a common backflow functional $N_I=\int_{\dot I>0}\dot I\,dt$. On the quantum side, we employ a fractional (Caputo) extension of a two-state dissipative model embedded by thermo-field dynamics (TFD), yielding a closed-form intrinsic entanglement component $b^{(\alpha)}_{qe}(t)=\frac14[E_\alpha(-\lambda^\alpha t^\alpha)]^2\sin^2(\omega t)$ and an integrated revival measure $N_{qe}$ that delineates a sharp boundary near $\alpha\simeq 1/2$ in the $(\alpha,\omega/\lambda)$ plane. On the classical side, we consider a three-state model whose Markov generator is promoted either to an exponential-kernel generalized master equation (with exact Markov embedding) or to a semi-Markov process with Erlang-2 waiting times. We quantify non-monotonicity by the entropy overshoot $\Delta H$ and KL-based diagnostics on the probability simplex. To strengthen the quantum--classical symmetry, we further introduce a \emph{fractional Mittag--Leffler memory kernel} in the classical dynamics and show that an analogous backflow transition emerges around $\alpha\simeq 1/2$, indicating that the boundary originates from the kernel's mathematical structure rather than from quantumness per se. Overall, our results provide a compact, model-agnostic route to classify non-Markovianity by phase diagrams of information backflow and to interpret them via a shared embedding narrative: memory stored in hidden degrees of freedom returns to the observed sector as non-monotonic information flow. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2601.18822 [quant-ph] (or arXiv:2601.18822v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.18822 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Koichi Nakagawa [view email] [v1] Sun, 25 Jan 2026 02:58:47 UTC (421 KB) Full-text links: Access Paper: View a PDF of the paper titled Phase Diagrams of Information Backflow: Unifying Entanglement Revivals and Entropy Overshoots in Minimal Non-Markovian Models, by Koichi NakagawaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)