Thermalization of Mutual Information in Hyperscaling Violating Backgrounds

TL;DR

This paper investigates how mutual information evolves during thermalization in hyperscaling violating backgrounds using holography, revealing the role of dynamical and scaling violating parameters in the process.

Contribution

It extends the understanding of mutual information thermalization to hyperscaling violating geometries, highlighting the influence of dynamical exponent and scaling violating parameter.

Findings

Mutual information exhibits specific time scaling behaviors during thermalization.

The dynamical exponent influences the pre-local-equilibration regime.

The scaling violating parameter can define an effective dimension.

Abstract

We study certain features of scaling behaviors of the mutual information during a process of thermalization, more precisely we extend the time scaling behavior of mutual information which has been discussed in \cite{Alishahiha:2014jxa} to time-dependent hyperscaling violating geometries. We use the holographic description of entanglement entropy for two disjoint system consisting of two parallel strips whose widths are much larger than the separation between them. We show that during the thermalization process, the dynamical exponent plays a crucial rule in reading the general time scaling behavior of mutual information (\emph{e.g.,} at the pre-local-equilibration regime). It is shown that the scaling violating parameter can be employed to define an effective dimension.