Einstein's equations and the pseudo-entropy of pseudo-Riemannian information manifolds
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Publication:6073497
DOI10.1007/S10714-023-03130-7arXiv2301.13017OpenAlexW4385077737MaRDI QIDQ6073497
Author name not available (Why is that?)
Publication date: 16 September 2023
Published in: (Search for Journal in Brave)
Abstract: Motivated by the corrected form of the entropy-area law, and with the help of von Neumann entropy of quantum matter, we construct an emergent spacetime by the virtue of the geometric language of statistical information manifolds. We discuss the link between Wald--Jacobson approaches of thermodynamic/gravity correspondence and Fisher pseudo-Riemannian metric of information manifold. We derive in detail Einstein's field equations in statistical information geometric forms. This results in finding a quantum origin of a positive cosmological constant that is founded on Fisher metric. This cosmological constant resembles those found in Lovelock's theories in a de Sitter background as a result of using the complex extension of spacetime and the Gaussian exponential families of probability distributions, and we find a time varying dynamical gravitational constant as a function of Fisher metric together with the corresponding Ryu-Takayanagi formula of such system. Consequently, we obtain a dynamical equation for the entropy in information manifold using Liouville-von Neumann equation from the Hamiltonian of the system. This Hamiltonian is suggested to be non-Hermitian, which corroborates the approaches that relate non-unitary conformal field theories to information manifolds. This provides some insights on resolving "the problem of time".
Full work available at URL: https://arxiv.org/abs/2301.13017
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