We study entropy corrections due to thermal fluctuations for asymptotically anti-de Sitter black holes in the grand canonical ensemble. To leading order, these can be expressed in terms of the black hole response coefficients via fluctuation moments. We also analyze entropy corrections due to mass and charge fluctuations of R-charged black holes, and our results indicate an universality in the logarithmic corrections to charged anti-de Sitter black hole entropy in various dimensions.