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Search Results (3)

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Keywords = restricted phase space formalism

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24 pages, 389 KiB  
Article
Dynamically Implementing the μ¯-Scheme in Cosmological and Spherically Symmetric Models in an Extended Phase Space Model
by Kristina Giesel and Hongguang Liu
Universe 2023, 9(4), 176; https://doi.org/10.3390/universe9040176 - 3 Apr 2023
Cited by 1 | Viewed by 1498
Abstract
We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given μ¯-scheme can be implemented dynamically. These models are constructed in the context of the relational formalism by using a canonical transformation [...] Read more.
We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given μ¯-scheme can be implemented dynamically. These models are constructed in the context of the relational formalism by using a canonical transformation on the extended phase space, which provides a Kuchař decomposition of the extended phase space. The resulting model can be understood as a gauge-unfixed model of a given μ¯-scheme. We use this formalism to investigate the restrictions to the allowed μ¯-scheme from this perspective and discuss the differences in the cosmological and spherically symmetric case. This method can be useful, for example, to obtain a μ¯-scheme in a top-down derivation from full LQG to symmetry-reduced effective models, where, for some models, only the μ0-scheme has been obtained thus far. Full article
(This article belongs to the Special Issue Loop Quantum Gravity: A Themed Issue in Honor of Prof. Abhay Ashtekar)
23 pages, 759 KiB  
Article
Restricted Phased Space Thermodynamics for Black Holes in Higher Dimensions and Higher Curvature Gravities
by Xiangqing Kong, Tao Wang, Zeyuan Gao and Liu Zhao
Entropy 2022, 24(8), 1131; https://doi.org/10.3390/e24081131 - 16 Aug 2022
Cited by 17 | Viewed by 1993
Abstract
The recently proposed restricted phase space thermodynamics is shown to be applicable to a large class of higher dimensional higher curvature gravity models coupled to Maxwell field, which are known as black hole scan models and are labeled by the spacetime dimension d [...] Read more.
The recently proposed restricted phase space thermodynamics is shown to be applicable to a large class of higher dimensional higher curvature gravity models coupled to Maxwell field, which are known as black hole scan models and are labeled by the spacetime dimension d and the highest order k of the Lanczos-Lovelock densities appearing in the action. Three typical example cases with (d,k)=(5,1),(5,2) and (6,2) are chosen as example cases and studied in some detail. These cases are representatives of Einstein-Hilbert, Chern-Simons and Born-Infield like gravity models. Our study indicates that the Einstein-Hilbert and Born-Infield like gravity models have similar thermodynamic behaviors, e.g., the existence of isocharge T−S phase transitions with the same critical exponents, the existence of isovoltage T−S transitions and the Hawking-Page like transitions, and the similar high temperature asymptotic behaviors for the isocharge heat capacities, etc. However, the Chern-Simons like (5,2)-model behaves quite differently. Neither isocharge nor isovoltage T−S transitions could occur and no Hawking-Page like transition is allowed. This seems to indicate that the Einstein-Hilbert and Born-Infield like models belong to the same universality class while the Chern-Simons like models do not. Full article
(This article belongs to the Special Issue Advances in Black Hole Thermodynamics)
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11 pages, 263 KiB  
Review
Group Entropies: From Phase Space Geometry to Entropy Functionals via Group Theory
by Henrik Jeldtoft Jensen and Piergiulio Tempesta
Entropy 2018, 20(10), 804; https://doi.org/10.3390/e20100804 - 19 Oct 2018
Cited by 17 | Viewed by 3954
Abstract
The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has [...] Read more.
The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalised entropies crucially depend on the number of allowed degrees of freedom N. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume W on N. We review the ensuing entropies, discuss the composability axiom and explain why group entropies may be particularly relevant from an information-theoretical perspective. Full article
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
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