Holographic Heat Engines, Entanglement Entropy, and Renormalization Group Flow

TL;DR

This paper connects conformal field theory RG flows with thermodynamic processes in hyperbolic black holes, showing how entanglement entropy and holographic heat engines reveal insights into the irreversibility and efficiency of these flows.

Contribution

It establishes a novel correspondence between RG flows in CFTs and thermodynamic processes of hyperbolic black holes, introducing holographic heat engines linked to entanglement entropy changes.

Findings

RG flows correspond to thermodynamic processes in the (p,V) plane.

Holographic heat engines relate to CFT deformations and flows.

Engine efficiencies depend on the ratio of degrees of freedom.

Abstract

We explore a fruitful connection between the physics of conformal field theories (CFTs) in d-dimensional Minkowski spacetime and the extended gravitational thermodynamics of hyperbolic black holes in (d+1)-dimensional anti-de Sitter spacetime. The CFTs are reduced on a region bounded by a sphere. We show that Renormalization Group (RG) flows between CFTs are specific thermodynamic processes in the (p,V) plane, where the irreversibility of coarse-graining flows from the ultraviolet to the infrared corresponds to the Second Law of thermodynamics, preventing heat from flowing from low temperature to high. We observe that holographic heat engines using the black holes as a working substance correspond to specific combinations of CFT flows and deformations. We construct three special engines whose net heat and work can be described in terms of changes of entanglement entropy across the sphere. Engine efficiencies emerge as simple functions of the ratio of the number of degrees of freedom of two CFTs.