Complexity Growth, Butterfly Velocity and Black hole Thermodynamics

TL;DR

This paper explores the relationship between butterfly velocity and complexity growth rate in black hole thermodynamics, linking these concepts through the Smarr formula and thermodynamic pressure, with validation across multiple models.

Contribution

It introduces a novel connection between butterfly velocity and complexity growth rate in black hole thermodynamics, considering the cosmological constant as pressure.

Findings

Established relations between butterfly velocity and complexity growth rate.

Validated the proposed relationship across several black hole models.

Linked thermodynamic pressure to complexity dynamics.

Abstract

We propose a connection between the butterfly velocity and the complexity growth rate in the context of thermodynamics of black holes where the cosmological constant is interpreted as thermodynamic pressure. According to the Smarr formula of black hole systems, there are different relations between butterfly velocity and complexity growth rate. The accuracy of this relationship has been checked for several models.