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.

我们研究了广义热力学第二定律的有效性，将巴罗熵应用于视界熵。前者源于这样一个事实，即黑洞表面可能由于量子引力效应而变形，由新指数\(\Delta \)量化。我们计算了充满物质和暗能量流体的宇宙中的熵时变，以及视界的相应量。我们证明，虽然在这种情况下\(\Delta =0\)，对应于通常的熵，由视界包围的熵加上视界本身的熵的总和始终是时间的非递减函数，因此在巴罗熵的情况下，广义热力学第二定律是有效的这不再是真的，而且根据宇宙的演化，广义的热力学第二定律可能会被违反。因此，为了不发生违反，标准 Bekenstein-Hawking 表达式的变形应该像预期的那样小。