Misanthropic entropy and renormalization as a communication channel

A central physical question is the extent to which infrared (IR) observations are sufficient reconstruct a candidate ultraviolet (UV) completion. We recast this as problem of communication, with messages encoded in field configurations UV being transmitted IR degrees freedom via noisy channel specified by renormalization group (RG) flow, noise generated coarse graining / decimation. present an explicit formulation these considerations terms lattice theory, where we show that "misanthropic entropy" -- mutual information obtained from decimating neighbors encodes lost marginalizing over tracing out freedom. Our apply both statistical theories well density matrix quantum systems, case, theory analysis amounts leading order approximation. As concrete example, focus on case 2D Ising model, misanthropic entropy detects onset phase transition at model critical point.