Relative Sofic Entropy
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In this dissertation, we focus on generalizing the concept of relative entropy of dynamical systems to sofic group actions. We introduce conditional sofic entropy of both topological and measurable dynamical systems. When the group is amenable, we prove one version of conditional sofic entropy is the classical conditional amenable entropy, and the other version of conditional sofic entropy is equal to the classical absolute amenable entropy in both topological and measurable settings. We also establish an addition formula for topological dynamical systems of sofic group actions, and the variational principle for two versions of conditional sofic entropy.