  We find the necessary and sufficient conditions for the entropy rate of the
system to be zero under any system-environment Hamiltonian interaction. We call
the class of system-environment states that satisfy this condition lazy states.
They are a generalization of classically correlated states defined by quantum
discord, but based on projective measurements of any rank. The concept of lazy
states permits the construction of a protocol for detecting global quantum
correlations using only local dynamical information. We show how quantum
correlations to the environment provide bounds to the entropy rate, and how to
estimate dissipation rates for general non-Markovian open quantum systems.
