The arrow of time and correlations in quantum physics

We discuss the arrow of time in terms of the increase of correlations between the system and its environment. Here we show that the existence of the arrow of time, based on deleting correlations, requires a strict absence of initial correlation between the system and the environment. We discuss our work in relation to other approaches addressing the same problem of entropy increase and emphasize similarities and differences. In particular, we comment on the link between initial correlations between the system and the environment and the resulting non complete positivity of the reduced state evolution.