https://doi.org/10.1140/epjc/s10052-026-15832-8
Regular Article - Theoretical Physics
Revisited apparent horizon entropy and GSL in modified gravity
Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Pasdaran Street, Sanandaj, Iran
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Received:
29
April
2026
Accepted:
10
May
2026
Published online:
3
June
2026
Abstract
This work presents a universal and revisited formalism for the entropy of the apparent horizon in modified gravity to investigate the validity of the Generalized Second Law (GSL) of thermodynamics. This revisited horizon entropy is constructed directly from the modified Friedmann equations in a Friedmann–Robertson–Walker (FRW) universe. The resulting entropy relation contains, beside the standard Bekenstein–Hawking term, an additional integral contribution that encodes the effective energy density and pressure generated by deviations from general relativity. Using this universal entropy formula, a compact expression for the GSL is derived. This formalism is then applied to some viable f(T) and f(R) gravity models, in order to re-evaluate the validity of the GSL as a function of redshift. The analysis demonstrates that including the integral term in the revisited entropy can relatively improve the late-time validity of the GSL for some of these models while living others unchanged, thereby reinforcing the profound connection between thermodynamics and gravity.
© The Author(s) 2026
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Funded by SCOAP3.
