Entropy and expansion

Understand

Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy.

• We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of independent random seeds.
• The inequality involves a constant characterizing the expansion properties of the system.
• Our results generalize to entropy inequalities used in recent work in invariant settings, including the edge-vertex inequality for factor-of-IID processes, Bowen's entropy inequalities, and Bollob\'as's entropy bounds in random regular graphs.