Regular Article - Theoretical Physics
The generalized second law of thermodynamics with Barrow entropy
National Observatory of Athens, Lofos Nymfon, 11852, Athens, Greece
2 CAS Key Laboratory for Researches in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, 230026, Hefei, Anhui, People’s Republic of China
3 School of Astronomy, School of Physical Sciences, University of Science and Technology of China, 230026, Hefei, People’s Republic of China
4 Academy of Athens, Research Center for Astronomy and Applied Mathematics, Soranou Efesiou 4, 11527, Athens, Greece
Accepted: 7 July 2021
Published online: 22 July 2021
We investigate the validity of the generalized second law of thermodynamics, applying Barrow entropy for the horizon entropy. The former arises from the fact that the black-hole surface may be deformed due to quantum-gravitational effects, quantified by a new exponent . We calculate the entropy time-variation in a universe filled with the matter and dark energy fluids, as well as the corresponding quantity for the apparent horizon. We show that although in the case , which corresponds to usual entropy, the sum of the entropy enclosed by the apparent horizon plus the entropy of the horizon itself is always a non-decreasing function of time and thus the generalized second law of thermodynamics is valid, in the case of Barrow entropy this is not true anymore, and the generalized second law of thermodynamics may be violated, depending on the universe evolution. Hence, in order not to have violation, the deformation from standard Bekenstein–Hawking expression should be small as expected.
© The Author(s) 2021
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