  We define and analyse the concept of entanglement production during the
evolution of a general quantum mechanical dissipative system. While it is
important to minimise entropy production in order to achieve thermodynamical
efficiency, maximising the rate of change of entanglement is important in
quantum information processing. Quantitative relations are obtained between
entropy and entanglement productions, under specific assumptions detailed in
the text. We apply these to the processes of dephasing and decay of
correlations between two initially entangled qubits. Both the Master equation
treatment as well as the higher Hilbert space analysis are presented. Our
formalism is very general and contains as special cases many reported
individual instance of entanglement dynamics, such as, for example, the
recently discovered notion of the sudden death of entanglement.
