Misanthropic Entropy and Renormalization as a Communication Channel

TL;DR

This paper models the process of IR observations as a communication channel affected by renormalization, introducing misanthropic entropy to quantify information loss and demonstrating its effectiveness in detecting phase transitions in the 2D Ising model.

Contribution

It formulates the IR-UV information transfer as a noisy communication channel using lattice field theory and introduces misanthropic entropy as a measure of information loss during renormalization.

Findings

Misanthropic entropy quantifies information loss in RG flow.

It detects the phase transition in the 2D Ising model.

The approach applies to both classical and quantum field theories.

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 neighbors -- encodes 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.