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

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2024-11, Vol.84 (11), p.1178-9, Article 1178
• Main Authors: Chen, Jianming, Chen, Gerui
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Black holes; Deformation; Elementary Particles; Energy conservation law; Entropy; Gravity; Hadrons; Heavy Ions; Investigations; Maximization; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Optimization; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum gravity; Regular Article; Spacetime; String Theory; Thermodynamics; Universe
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-024-13517-8

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 = π sin A 8 G N / sin π 2 N , where N = L q 2 / L p 2 is the q-deformation parameter, L p denotes the Planck length, and 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, 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.