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Classical and quantum geometric information flows and entanglement of relativistic mechanical systems

  • Sergiu I. VacaruEmail author
  • Laurenţiu Bubuianu
Article
  • 21 Downloads

Abstract

This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange–Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigori Perelman’s entropy for geometric flows and associated statistical thermodynamic systems to the quantum von Neumann entropy, classical and quantum relative and conditional entropy, mutual information, etc. We formulate the concept of the entanglement entropy of quantum geometric information flows and study properties and inequalities for quantum, thermodynamic and geometric entropies characterizing such systems.

Keywords

Perelman W-entropy Quantum geometric information flows Relativistic Lagrange-Hamilton mechanics Entanglement entropy of quantum geometric information flows 

Mathematics Subject Classification

53C44 53C50 53C80 81P45 82D99 83C15 83C55 83C99 83D99 35Q75 37J60 37D35 

Notes

Acknowledgements

This research develops the former programs partially supported by IDEI, PN-II-ID-PCE-2011-3-0256, CERN 2012-2014, DAAD-2015 and QGR 2016-2017 and contains certain results for new grant proposals. The UAIC affiliation for S. V. refers to a Project IDEI hosted by that University during 2012–2015, when the bulk of geometric ideas and methods of this and partner works were elaborated (to put a relevant co-/affiliation for further related results was the condition of that grant). Performing rigorous mathematical proofs and respective manuscripts request many years of technical work and further collaborations. S. V. is grateful to D. Singleton, S. Rajpoot and P. Stavrinos for collaboration and supporting his research on geometric methods in physics.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Physics DepartmentCalifornia State University at FresnoFresnoUSA
  2. 2.Department of Theoretical Physics and Computer Modelling, Institute of Applied-Physics and Computer SciencesYuriy Fedkovych Chernivtsi National UniversityChernivtsiUkraine
  3. 3.Project IDEI - 2011University “Al. I. Cuza”IaşiRomania
  4. 4.SRTV - Studioul TVR IaşiIaşiRomania
  5. 5.University ApolloniaIaşiRomania

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