  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 $\Delta$. 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 $\Delta=0$, 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.
