Note on stability and holographic subregion complexity

TL;DR

This paper investigates how anisotropy affects holographic subregion complexity during a phase transition, proposing informational and computational interpretations to distinguish stable and unstable solutions.

Contribution

It introduces new informational and computational perspectives to identify stable and unstable solutions in anisotropic holographic models with phase transitions.

Findings

Anisotropy reduces holographic subregion complexity.

Complexity decreases for mixed states as temperature increases.

Proposed interpretations link complexity to information and computational resources.

Abstract

We study holographic subregion complexity in a spatially anisotropic field theory, which expresses a confinement-deconfinement phase transition. Its holographic dual is a five-dimensional anisotropic holographic model characterized by a Van der Waals-like phase transition between small and large black holes. We propose a new interpretation from the informational perspective to determine the stable and unstable thermodynamically solutions. According to this proposal, the states which need (more) less information to be specified characterize the (un) stable solutions. We similarly offer an interpretation to determine the stable and unstable solutions based on the resource of a computational machine, such that the solutions are (un) stable if computational resource (decreases) increases with the increase of temperature. We observe that the effect of anisotropy on holographic subregion complexity is decreasing. This decreasing effect can be interpreted by considering a whole closed system consisting of the state and its environment in which the complexity of the mixed state decreases and complexity of the environment increases.