Exact Renormalization Groups as a form of Entropic Dynamics

TL;DR

This paper demonstrates that exact renormalization group equations can be derived using entropic methods, framing RG flow as entropic dynamics of field configurations with an information-theoretic interpretation.

Contribution

It introduces a novel entropic derivation of exact RG equations, linking renormalization group flow to information theory and entropic dynamics.

Findings

RG equations derived via entropic methods

RG flow interpreted as entropic dynamics

Establishes a link between RG and information theory

Abstract

The Renormalization Group (RG) is a set of methods that have been instrumental in tackling problems involving an infinite number of degrees of freedom. What all these methods have in common -- which is what explains their success -- is that they allow a systematic search for those degrees of freedom that happen to be relevant to the phenomena in question. In the standard approaches the RG transformations are implemented by either coarse graining or by changes of variables. When these transformations are infinitesimal the formalism can be described as a continuous dynamical flow in a fictitious time parameter. It is generally the case that these exact RG equations are functional diffusion equations. In this paper we show that the exact RG equations can be derived using entropic methods. The RG flow is then described as a form of entropic dynamics of field configurations. Although equivalent to other versions of the RG, in this approach the RG transformations receive a purely inferential interpretation that establishes a clear link to information theory.