Waking and Scrambling in Holographic Heating up

Abstract

We consider a holographic model of the heating up process. As a dual background we take a geometry describing thin shell accretion on a black brane. We find explicitly the time evolution of the mutual information during the non-equlibrium heating process from the initial temperature $T_i$ to the final temperature $T_f$ for the system of two intervals in the 1+1 dimensional case. We calculate widths and separation of twointervals for which the time dependence of the mutual information has the bell-like form, i.e. it starts from zero value at the wake up time, then reaches a maximal value and vanishes at the scrambling time. This form of the mutual information evolution was previously found in photosynthesis. The zone of the bell-like configurations exists for small distances $x<\log 2/2\pi T_i$ only for the particular interval sizes. For $x$ large enough, i.e. $x>>\log 2/2\pi T_i$, it exists only for large enough interval sizes and this zone becomes more narrow when $T_i$ increases and becomes larger with increasing of $T_f$.