# Holographic complexity of local quench at finite temperature

## TL;DR

This paper investigates how holographic complexity evolves after a local perturbation at finite temperature, comparing two conjectures and revealing growth behaviors, saturation, and violations of the Lloyd bound.

## Contribution

It provides a comparative analysis of CA and CV holographic complexity after local quench at finite temperature, highlighting growth patterns and bounds violations.

## Key findings

- CV complexity exhibits unbounded linear growth at late times.
- CA complexity shows linear growth with rapid saturation.
- Finite temperature causes violation of the Lloyd bound for CA complexity.

## Abstract

This paper is devoted to the study of the evolution of holographic complexity after a local perturbation of the system at finite temperature. We calculate the complexity using both the complexity=action(CA) and the complexity=volume(CA) conjectures and find that the CV complexity of the total state shows the unbounded late time linear growth. The CA computation shows linear growth with fast saturation to a constant value. We estimate the CV and CA complexity linear growth coefficients and show, that finite temperature leads to violation of the Lloyd bound for CA complexity. Also it is shown that for composite system after the local quench the state with minimal entanglement may correspond to the maximal complexity.