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We study the effect of inhomogeneity, which is induced by the graviton massin massive gravity, on the mutual information and the chaotic behavior of a2+1-dimensional field theory from the gauge/gravity duality. When the system isnear-homogeneous, the mutual information increases as the graviton mass grows.However, when the system is far from homogeneity, the mutual informationdecreases as the graviton mass increases. By adding the perturbations of energyinto the system, we investigate the dynamical mutual information in the shockwave geometry. We find that the greater perturbations disrupt the mutualinformation more rapidly, which resembles the butterfly effect in chaos theory.Besides, the greater inhomogeneity reduces the dynamical mutual informationmore quickly just as in the static case.

Influence of inhomogeneities on holographic mutual information and butterfly effect