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

Jianming Chen; Gerui Chen

doi:10.1140/epjc/s10052-024-13517-8

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 1178
https://doi.org/10.1140/epjc/s10052-024-13517-8

Regular Article

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

Jianming Chen and Gerui Chen^a

College of Electronic Information and Physics, Central South University of Forestry and Technology, 410004, Changsha, China

^a t20152277@csuft.edu.cn

Received: 4 June 2024
Accepted: 20 October 2024
Published online: 19 November 2024

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 $S = π sin (\frac{A}{8 G N}) / sin (\frac{π}{2 N})$ $S = \pi \sin \left( \frac{A}{8G\mathcal {N}} \right) /\sin \left( \frac{\pi }{2\mathcal {N}}\right)$ , where $N = L_{q}^{2} / L_{p}^{2}$ $\mathcal {N}=L_q^2/L_{p}^2$ 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, $d E = T d S + W d V$ $$ dE = TdS + WdV $$ . 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.

© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.