Holographic Complexity and Thermodynamic Volume

TL;DR

This paper explores the relationship between holographic complexity and thermodynamic volume in rotating black holes, proposing that thermodynamic volume, rather than entropy, governs the complexity of formation.

Contribution

It introduces a novel perspective linking complexity of formation to thermodynamic volume and extends known results to broader black hole settings.

Findings

Complexity of formation is controlled by thermodynamic volume.

For large black holes, complexity is bounded below by entropy.

The proposal generalizes existing entropy-based results.

Abstract

We study the holographic complexity conjectures for rotating black holes, uncovering a relationship between the complexity of formation and the thermodynamic volume of the black hole. We suggest that it is the thermodynamic volume and not the entropy that controls the complexity of formation of large black holes in both the Complexity Equals Action and Complexity Equals Volume proposals in general. Our proposal reduces to known results involving the entropy in settings where the thermodynamic volume and entropy are not independent, but has broader scope. Assuming a conjectured inequality is obeyed by the thermodynamic volume, we establish that the complexity of formation is bounded from below by the entropy for large black holes.