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However, for Gauss-Bonnet couplings $\\lambda$, larger than a specific value, but still allowed by causality, we observe a violation of the inequality $\\frac{\\partial}{{\\partial q}}\\left({\\frac{{q - 1}}{q}S_q(\\mu,\\lambda)} \\right) \\ge 0$, which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. 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