Thermodynamic and Holographic Information Dual to Volume

TL;DR

This paper explores the relationship between thermodynamic volume and information measures like fidelity susceptibility and holographic complexity in AdS spacetimes, establishing a link between thermodynamics and holographic information.

Contribution

It introduces a regularization method for fidelity susceptibility and complexity, revealing their distinct behaviors and connecting them to thermodynamic volume in holographic duality.

Findings

Regularized fidelity susceptibility matches thermodynamic volume behavior.

Regularized complexity exhibits a different behavior from volume.

Establishes a connection between thermodynamics and holographic information.

Abstract

In this paper, we will analyze the connection between the fidelity susceptibility, the holographic complexity and the thermodynamic volume. We will regularize the fidelity susceptibility and the holographic complexity by subtracting the contribution of the background AdS spacetime from the deformation of the AdS spacetime. It will be demonstrated that this regularized fidelity susceptibility has the same behavior as the thermodynamic volume and that the regularized complexity has a very different behavior. As the information dual to different volumes in the bulk would be measured by the fidelity susceptibility and the holographic complexity, this paper will establish a connection between thermodynamics and information dual to a volume.