Relation between the Dynamics of the Reduced Purity and Correlations

A general property of the relation between the dynamics of the reduced purity and correlations is investigated in quantum mechanical systems. We show that a non-zero time-derivative of the reduced purity of a system implies the existence of non-zero correlations with its environment under any unbounded Hamiltonians with finite variance. This shows the role of local dynamical information on the correlations, as well as the role of correlations in the mechanism of purity change.Comment: 7 page