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      Binary Data Matrix Theory

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      research-article
        1 ,
      ScienceOpen Preprints
      ScienceOpen
      Quantum Liouville equation, metric compatibility condition, Joint probability, Binary Data Matrix, Ricci flow
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            Abstract

            In this paper after introducing a model of binary data matrix (BDM) for physical parameters of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition k g ij =0 while covariant derivative of metric tensor has been calculated respect to Wick rotated time or spatial coordinates. After deriving a formula for expected energy per particles, we prove the equality of this expected energy with local scalar curvature of related manifold. We show the compatibility of BDM model with Hamilton-Jacobi formalism and canonical forms. On the basis of the model, I derive the Ricci flow like dynamics as the governing dynamics and subsequently derive the action of BDM model and Einstein field equations. Given examples clarify the compatibility of the results with well-known principles such as equipartition energy principle and Landauer’s principle. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry. Finally, we conclude a “bit density principle” which predicts the Planck equation, De Broglie wave particle relation, E=m c 2 , Beckenstein bound and Bremermann limit.

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            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            23 February 2022
            Affiliations
            [1 ] Tehran Azad University, Tehran, Iran
            Author notes
            Article
            10.14293/S2199-1006.1.SOR-.PP87C3T.v1
            3242a20e-2f70-41ee-aa63-fe850a73da06

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .


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            Physics
            Quantum Liouville equation,metric compatibility condition,Joint probability,Binary Data Matrix,Ricci flow

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