Waking and scrambling in holographic heating up

Using holographic methods, we study the heating up process in quantum field theory. As a holographic dual of this process, we use absorption of a thin shell on a black brane. We find the explicit form of the time evolution of the quantum mutual information during heating up from the temperature $T_{\mathrm i}$ to the temperature $T_{\mathrm f}$ in a system of two intervals in two-dimensional space–time. We determine the geometric characteristics of the system under which the time dependence of the mutual information has a bell shape: it is equal to zero at the initial instant, becomes positive at some subsequent instant, further attains its maximum, and again decreases to zero. Such a behavior of the mutual information occurs in the process of photosynthesis. We show that if the distance $x$ between the intervals is less than $\ln 2/2\pi T_{\mathrm i}$, then the evolution of the holographic mutual information has a bell shape only for intervals whose lengths are bounded from above and below. For sufficiently large $x$, i.e., for $x>\ln2/2\pi T_{\mathrm i}$, the bell-like shape of the time dependence of the quantum mutual information is present only for sufficiently large intervals. Moreover, the zone narrows as $T_{\mathrm i}$ increases and widens as $T_{\mathrm f}$ increases.