Thermodynamics analysis of black hole through modified entropies by applying Hawking evaporation phenomenon
Rani S. Majeed A. Azhar N. Yesmakhanova K. Myrzakulov N. Shaymatov S. Jawad A.
February 2026Elsevier B.V.
Physics of the Dark Universe
2026#51
In this work, we examine how well-known entropy corrections influence the thermodynamic evolution of black holes by employing two complementary approaches. In the first part, we incorporate an exponential modification to the area-entropy relation motivated by quantum-gravitational effects. Using this corrected entropy, we derive the corresponding mass evolution, Gibbs and Helmholtz free energies, radiation law, and specific heat within the semiclassical evaporation framework. The results show that exponential corrections suppress entropy growth at small horizon scales, reduce the energy emission rate at high temperatures, and intensify the negative specific heat, indicating enhanced thermodynamic instability near the final evaporation stage. In the second part, we explore a generalized singularity-free Helmholtz free energy model that captures non-extensive and quantum-statistical deviations from classical black-hole thermodynamics. The corrected entropy, partition function, and related thermodynamic quantities are derived and analyzed for different values of the correction parameters. The graphical behavior reveals that these generalized corrections tend to moderate evaporation, extend the lifetime of the black hole, and improve the stability of the thermodynamic phase space.
Black hole thermodynamics , Exponential entropy correction , Generalized free energy , Helmholtz free energy , Quantum gravity
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Department of Mathematics, COMSATS University Islamabad, Lahore-Campus, Lahore, 54000, Pakistan
Department of Mathematics, National University of Modern Languages (NUML), Lahore-Campus, Lahore, 54000, Pakistan
Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan
L. N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan
Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, Tashkent, 100000, Uzbekistan
University of Tashkent for Applied Sciences, Str. Gavhar 1, Tashkent, 100149, Uzbekistan
Tashkent State Technical University, Tashkent, 100095, Uzbekistan
Western Caspian University, Baku, AZ1001, Azerbaijan
Department of Mathematics
Department of Mathematics
Research Center of Astrophysics and Cosmology
L. N. Gumilyov Eurasian National University
Institute of Fundamental and Applied Research
University of Tashkent for Applied Sciences
Tashkent State Technical University
Western Caspian University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026