Relative information entropy in cosmology: The problem of information entanglement

Czinner, Viktor G.; Mena, Filipe C.

doi:10.1016/j.physletb.2016.04.043

Cited by 19 publications

(17 citation statements)

References 31 publications

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“…Specific models on how to compute the λ parameter value for various gravitational problems are actively investigated; see e.g. [55] for a quantum geometric approach to the black hole problem, and [58] for the case of the problem of information entropy in cosmology. In the latter work, as an effective model, the λ parameter of the Tsallis/Rényi relative entropy has been defined in a geometric way in order to describe the causal connection between a cosmological domain and its surroundings during the cosmic evolution.…”

Section: Discussionmentioning

confidence: 99%

“…It has been found that the corresponding Padmanabhan's "holographic equipartition law" [57] can result an effective cosmological constant in the model. Similar considerations have also been applied to describe the relative information entropy measure inside compact domains of an inhomogeneous universe [58], and an explicit geometric model has been proposed to compute the q-parameter of the Rényi entropy in order to measure the effects of the gravitational entanglement problem.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

Czinner

Iguchi

2017

Eur. Phys. J. C

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Thermodynamics of rotating black holes described by the Rényi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the Rényi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a HawkingPage transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the Rényi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

Czinner

Iguchi

2017

Eur. Phys. J. C

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“…The gravitational entropy which is defined in this way is conjectured to grow in generic situations due to negative feedback of open gravitational systems, which is proved to hold for linear perturbations of an Einstein-de Sitter background model, and exact Lemaître-Tolman models [17]. It has also been show that in the cosmological context the Kullback-Leibler relative information entropy can be well approximated by the Rényi relative entropy [18], and that it can be linked to Weyl curvature [19]. To distinguish this approach from the other, let us denote the entropy defined based on the information entropy as the HBM gravitational entropy and the gravitational entropy that is derived from the Bel-Robinson tensor as the CET gravitational entropy.…”

Section: Introductionmentioning

confidence: 87%

Gravitational entropy and the cosmological no-hair conjecture

Bolejko

2018

Phys. Rev. D

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The gravitational entropy and no-hair conjectures seems to predict contradictory future states of our Universe. The growth of the gravitational entropy is associated with the growth of inhomogeneity, while the no-hair conjecture argues that a universe dominated by dark energy should asymptotically approach a homogeneous and isotropic de Sitter state. The aim of this paper is to study these two conjectures. The investigation is based on the Simsilun simulation, which simulates the universe using the approximation of the Silent Universe. The Silent Universe is a solution to the Einstein equations that assumes irrotational, non-viscous, and insulated dust, with vanishing magnetic part of the Weyl curvature. The initial conditions for the Simsilun simulation are sourced from the Millennium simulation, which results with a realistically appearing but relativistic at origin simulation of a universe. The Simsilun simulation is evolved from the early universe (t = 25 Myr) till far future (t = 1000 Gyr). The results of this investigation show that both conjectures are correct. On global scales, a universe with a positive cosmological constant and non-positive spatial curvature does indeed approach the de Sitter state. At the same time it keeps generating the gravitational entropy. *

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“…Information entropy (Czinner and Mena 2016;Duan 2012;Rao 2006;Tsujimura and Gen 1999;Shannon 1948) represents the amount of information contained in a system state. Information entropy accurately reflects the system complexity variation.…”

Section: Rms Complexity Analysismentioning

confidence: 99%

Reconfiguration point decision method based on dynamic complexity for reconfigurable manufacturing system (RMS)

et al. 2017

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To address the problem of how to identify the best time to implement reconfiguration for the reconfigurable manufacturing system (RMS), a dynamic complexity-based RMS reconfiguration point decision method is proposed. This method first identifies factors that affect RMS dynamic complexity (including both positive and negative complexity) at the machine tool and manufacturing cell levels. Next, based on information entropy theory, a quantitative model for RMS dynamic complexity is created, which is solved via state probability analysis for processing capability and the processing function. This model is combined with cusp catastrophe theory to establish an RMS reconfiguration decision model. Both positive and negative complexity are control variables for cusp catastrophe. Cusp catastrophe's state condition is used to identify RMS state catastrophe at the final stage of production. This catastrophe point is the RMS reconfiguration point. Finally, the case study result shows that this method can effectively identify the RMS state catastrophe moment so that system reconfiguration is implemented promptly to improve RMS's responsiveness to the market.

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Relative information entropy in cosmology: The problem of information entanglement

Cited by 19 publications

References 31 publications

Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

Gravitational entropy and the cosmological no-hair conjecture

Reconfiguration point decision method based on dynamic complexity for reconfigurable manufacturing system (RMS)

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