爱因斯坦方程与伪黎曼信息流形的伪熵

IF 2.1 4区 物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS General Relativity and Gravitation Pub Date : 2023-07-21 DOI:10.1007/s10714-023-03130-7
Hassan Alshal
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引用次数: 0

摘要

在熵面积定律的修正形式的激励下,借助量子物质的冯·诺伊曼熵,我们借助统计信息流形的几何语言构建了一个涌现时空。讨论了热力学/重力对应的Wald和Jacobson方法与信息流形的Fisher伪黎曼度量之间的联系。我们详细地导出了统计信息几何形式的爱因斯坦场方程。结果发现了基于费雪度规的正宇宙常数的量子起源。这个宇宙学常数类似于在德西特背景下使用时空复扩展和高斯指数族概率分布的洛夫洛克理论中发现的宇宙学常数,我们发现了一个随时间变化的动态引力常数,作为Fisher度规的函数,以及相应的Ryu-Takayanagi公式。因此,我们从系统的哈密顿量出发,利用liouvil_von Neumann方程,得到了信息流形中熵的动力学方程。这个哈密顿量被认为是非厄米量,这证实了将非酉共形场理论与信息流形联系起来的方法。这为解决“时间问题”提供了一些见解。
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Einstein’s equations and the pseudo-entropy of pseudo-Riemannian information manifolds

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 and 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”.

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来源期刊
General Relativity and Gravitation
General Relativity and Gravitation 物理-天文与天体物理
CiteScore
4.60
自引率
3.60%
发文量
136
审稿时长
3 months
期刊介绍: General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation. It welcomes in particular original articles on the following topics of current research: Analytical general relativity, including its interface with geometrical analysis Numerical relativity Theoretical and observational cosmology Relativistic astrophysics Gravitational waves: data analysis, astrophysical sources and detector science Extensions of general relativity Supergravity Gravitational aspects of string theory and its extensions Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations Quantum field theory in curved spacetime Non-commutative geometry and gravitation Experimental gravity, in particular tests of general relativity The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.
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