Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropy

Abstract According to the quantum deformation approach to quantum gravity, the thermodynamical entropy of a quantum-deformed (q-deformed) black hole with horizon area A established by Jalalzadeh is expressed as $$S = \pi \sin \left( \frac{A}{8G\mathcal {N}} \right) /\sin \left( \frac{\pi }{2\mathcal...

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Main Authors: Jianming Chen, Gerui Chen
Format: Article
Language:English
Published: SpringerOpen 2024-11-01
Series:European Physical Journal C: Particles and Fields
Online Access:https://doi.org/10.1140/epjc/s10052-024-13517-8
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author Jianming Chen
Gerui Chen
author_facet Jianming Chen
Gerui Chen
author_sort Jianming Chen
collection DOAJ
description Abstract According to the quantum deformation approach to quantum gravity, the thermodynamical entropy of a quantum-deformed (q-deformed) black hole with horizon area A established by Jalalzadeh is expressed as $$S = \pi \sin \left( \frac{A}{8G\mathcal {N}} \right) /\sin \left( \frac{\pi }{2\mathcal {N}}\right) $$ S = π sin A 8 G N / sin π 2 N , where $$\mathcal {N}=L_q^2/L_{p}^2$$ N = L q 2 / L p 2 is the q-deformation parameter, $$L_{p}$$ L p denotes the Planck length, and $$L_q$$ L q denotes the quantum-deformed cosmic apparent horizon distance. In this paper, assuming that the q-deformed entropy is associated with the apparent horizon of the Friedmann–Robertson–Walker (FRW) universe, we derive the modified Friedmann equation from the unified first law of thermodynamics, $$ dE = TdS + WdV $$ d E = T d S + W d V . And this one obtained is in line with the modified Friedmann equation derived from the law of emergence proposed by Padmanabhan. It clearly shows the connection between the law of emergence and thermodynamics. We further investigate the constraints of entropy maximization in the framework of the q-deformed horizon entropy, and the results demonstrate the consistency of the law of emergence with the maximization of the q-deformed horizon entropy.
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spelling doaj-art-23537f1673b54a6db3b926d3a52094f42024-12-29T12:44:13ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-11-0184111910.1140/epjc/s10052-024-13517-8Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropyJianming Chen0Gerui Chen1College of Electronic Information and Physics, Central South University of Forestry and TechnologyCollege of Electronic Information and Physics, Central South University of Forestry and TechnologyAbstract According to the quantum deformation approach to quantum gravity, the thermodynamical entropy of a quantum-deformed (q-deformed) black hole with horizon area A established by Jalalzadeh is expressed as $$S = \pi \sin \left( \frac{A}{8G\mathcal {N}} \right) /\sin \left( \frac{\pi }{2\mathcal {N}}\right) $$ S = π sin A 8 G N / sin π 2 N , where $$\mathcal {N}=L_q^2/L_{p}^2$$ N = L q 2 / L p 2 is the q-deformation parameter, $$L_{p}$$ L p denotes the Planck length, and $$L_q$$ L q denotes the quantum-deformed cosmic apparent horizon distance. In this paper, assuming that the q-deformed entropy is associated with the apparent horizon of the Friedmann–Robertson–Walker (FRW) universe, we derive the modified Friedmann equation from the unified first law of thermodynamics, $$ dE = TdS + WdV $$ d E = T d S + W d V . And this one obtained is in line with the modified Friedmann equation derived from the law of emergence proposed by Padmanabhan. It clearly shows the connection between the law of emergence and thermodynamics. We further investigate the constraints of entropy maximization in the framework of the q-deformed horizon entropy, and the results demonstrate the consistency of the law of emergence with the maximization of the q-deformed horizon entropy.https://doi.org/10.1140/epjc/s10052-024-13517-8
spellingShingle Jianming Chen
Gerui Chen
Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropy
European Physical Journal C: Particles and Fields
title Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropy
title_full Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropy
title_fullStr Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropy
title_full_unstemmed Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropy
title_short Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropy
title_sort emergence of cosmic space and horizon thermodynamics in the context of the quantum deformed entropy
url https://doi.org/10.1140/epjc/s10052-024-13517-8
work_keys_str_mv AT jianmingchen emergenceofcosmicspaceandhorizonthermodynamicsinthecontextofthequantumdeformedentropy
AT geruichen emergenceofcosmicspaceandhorizonthermodynamicsinthecontextofthequantumdeformedentropy