Information upper bound for McKean-Vlasov stochastic differential equations.

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We develop an information-theoretic framework to quantify information upper bound for the probability distributions of the solutions to the McKean-Vlasov stochastic differential equations. More precisely, we derive the information upper bound in terms of Kullback-Leibler divergence, which characterizes the entropy of the probability distributions of the solutions to McKean-Vlasov stochastic differential equations relative to the joint distributions of mean-field particle systems. The order of information upper bound is also figured out.