Abstract
In this paper, we present the entropy relations and bounds of Banados–Teitelboim–Zanelli (BTZ) black hole in two models of gravity's rainbow. Because of the effect of gravity's rainbow, one can find that the entropy product and sum both lost their universality and become mass-dependent. On the other hand, comparing the entropy bound of event horizon to the BTZ case, it is shown that the angular momentum [Formula: see text] enlarges the entropy bound while the gravity's rainbow parameter [Formula: see text] diminishes it. For the entropy bound of Cauchy horizon, the gravity's rainbow parameter [Formula: see text] enlarges it at the large [Formula: see text] limit, while [Formula: see text] diminishes it at the small [Formula: see text] limit. These suggest some clues on the geometrical origin of black hole entropy bounds.
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