Complexity and uncomplexity during energy injection

TL;DR

This paper investigates the evolution of holographic subregion complexity in a strongly coupled field theory near a critical point, exploring its behavior, interpretations, and relation to critical phenomena and microstates.

Contribution

It introduces a dual perspective on complexity in AdS/CFT, analyzing its evolution near critical points and proposing interpretations consistent with the second law of complexity.

Findings

Complexity decreases during certain evolution phases.

Complexity serves as a probe for the dynamical critical exponent.

Different concepts of complexity yield contrasting interpretations.

Abstract

We consider a strongly coupled field theory with a critical point and nonzero chemical potential at finite temperature, which is dual to an asymptotically AdS charged black hole. We study the evolution of the rescaled holographic subregion complexity near and far from the critical point. We explain two distinct concepts of complexity in this theory and discuss that the state under study is complex based on how much information is needed to specify the state and is simple according to how many operations have to be done to reach the state. It has been reported before that time evolution of holographic subregion complexity contradicts the second law of complexity in these AdS-Vaidya-like geometries, but we try to provide a compatible interpretation. We justify decreasing of complexity using an increasing number of microstates of the mixed state and speculate about the description of the relative complexity of the initial state and the final state as a resource. We propose that in this process complexity of the mixed state decreases and complexity of the environment increases. We also observe that in this model, the rescaled holographic subregion complexity is a good observable for probing the dynamical critical exponent.