Several authors have hypothesized that completely positive maps should provide the means for generalizing quantum dynamics. In a critical analysis of that proposal, we show that such maps are incompatible with the standard phenomenological theory of spin relaxation and that the theoretical argument which has been offered as justification for the hypothesis is fallacious.

This paper explores the possibility that linear dynamical maps might be used to describe the energy-conserving, entropy-increasing motions which occur in closed thermodynamic systems as they approach canonical thermal equilibrium. ForN-level quantum systems withN>2, we prove that no such maps exist which are independent of the initial state.

In this rejoinder to a critique by Raggio and Primas of our paper, “On Completely Positive Maps in Generalized Quantum Dynamics,” we acknowledge that, contrary to our original assertion, the Bloch equations are indeed completely positive. We then explain briefly why this modification of our analysis does not alter its main conclusions.