Misanthropic Entropy and Renormalization as a Communication Channel

Abstract

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

Disorder Averaging and its UV (Dis)Contents

“…This is related to the broader question of how well a low energy observer can ever hope to reconstruct a given UV completion, see, e.g.,[14,[40][41][42][43][44] as well as[45][46][47][48][49][50][51][52].…”

On the Dynamics of Inference and Learning

“…The second order expansion in θ i of the KL divergence then yields the Fisher information metric which forms the basis for information geometry [9,10]. (See [11][12][13][14][15][16][17][18][19][20][21][22] for contemporary appearances of the information metric in statistical inference and its relevance to quantum field theory and string theory. )…”