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 $$S = \pi \sin \left( \frac{A}{8G\mathcal {N}} \right) /\sin \left( \frac{\pi }{2\mathcal...
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2024-11-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-024-13517-8 |
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| author | Jianming Chen Gerui Chen |
| author_facet | Jianming Chen Gerui Chen |
| author_sort | Jianming Chen |
| collection | DOAJ |
| description | Abstract According to the quantum deformation approach to quantum gravity, the thermodynamical entropy of a quantum-deformed (q-deformed) black hole with horizon area A established by Jalalzadeh is expressed as $$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 $$ d E = T d S + W d V . And this one obtained is in line with the modified Friedmann equation derived from the law of emergence proposed by Padmanabhan. It clearly shows the connection between the law of emergence and thermodynamics. We further investigate the constraints of entropy maximization in the framework of the q-deformed horizon entropy, and the results demonstrate the consistency of the law of emergence with the maximization of the q-deformed horizon entropy. |
| format | Article |
| id | doaj-art-23537f1673b54a6db3b926d3a52094f4 |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-23537f1673b54a6db3b926d3a52094f42024-12-29T12:44:13ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-11-0184111910.1140/epjc/s10052-024-13517-8Emergence of cosmic space and horizon thermodynamics in the context of the quantum-deformed entropyJianming Chen0Gerui Chen1College of Electronic Information and Physics, Central South University of Forestry and TechnologyCollege of Electronic Information and Physics, Central South University of Forestry and TechnologyAbstract According to the quantum deformation approach to quantum gravity, the thermodynamical entropy of a quantum-deformed (q-deformed) black hole with horizon area A established by Jalalzadeh is expressed as $$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 |