Physical Generalizations of the Renyi Entropy

TL;DR

This paper introduces a new generalization of Renyi entropy inspired by thermodynamics, applicable to conformal field theories and potentially useful for quantum and classical information analysis.

Contribution

It proposes a natural extension of Renyi entropy based on gravitational thermodynamics and RG flow, with derivations for d=2 and broader potential applications.

Findings

New generalized Renyi entropy framework derived from thermodynamics

Application to conformal field theories in various dimensions

Potential implications for quantum and classical information theory

Abstract

We present a new type of generalization of the Renyi entropy that follows naturally from its representation as a thermodynamic quantity. We apply it to the case of d-dimensional conformal field theories (CFTs) reduced on a region bounded by a sphere. It is known how to compute their Renyi entropy as an integral of the thermal entropy of hyperbolic black holes in (d+1)-dimensional anti-de Sitter spacetime. We show how this integral fits into the framework of extended gravitational thermodynamics, and then point out the natural generalization of the Renyi entropy that suggests itself in that light. In field theory terms, the new generalization employs aspects of the physics of Renormalization Group (RG) flow to define a refined version of the reduced vacuum density matrix. For d=2, it can be derived directly in terms of twist operators in field theory. The framework presented here may have applications beyond this context, perhaps in studies of both quantum and classical information theoretic properties of a variety of systems.