In the context of an Open Quantum System (OQS) i.e. a quantum system coupled to a quantum environment, what is really meant by information backflow from the environment to the system? I'm newly exposed to this field and learning basic standard stuff related to the formalism. Looking forward to a simple explanation.
More details I came across this term in an ICTP video lecture on open quantum systems by Ines de Vega (here, around $4.40$mins). The phrase 'information backflow' was used as one of the qualifiers that characterize non-Markovian dynamics. My impression is that if we start with the system in a pure state at time $t=0$, the interaction will establish entanglement between the system and the bath. Therefore, at $t>0$ the reduced density matrix for the system will not satisfy $\rho^2_S(t)=\rho_S(t)$, even though initially $\rho^2_S(0)=\rho_S(0)$. Is this referred to as information outflow? Then, what's backflow?