Physical Generalizations of the Renyi Entropy

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.

19 pages. 5 multi-component figures

References in corpus (4)

• Towards a derivation of holographic entanglement entropy
• Twist operators in higher dimensions
• Charged Renyi entropies and holographic superconductors
• Holographic Heat Engines, Entanglement Entropy, and Renormalization Group Flow

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• Specific Heats and Schottky Peaks for Black Holes in Extended Thermodynamics
• Ruppeiner curvature along a renormalization group flow
• Perspective on Physical Interpretations of Rényi Entropy in Statistical Mechanics
• Localized thermal states and negative energy
• Extended Holographic Rényi Entropy and hyperbolic black hole with scalar hair