Detailed Balance and Quantum Dynamical Maps

by W. A. Majewski and R. F. Streater, J. Phys., A31, 7981-7995, 1998.

ABSTRACT

Let T be a stochastic map on a C*$-algebra A, and omega a faithful state. Let pi_{omega}(T) be the induced action of T on the GNS (=Gelfand-Naimark-Segal) Hilbert space cal A_{omega}, and pi_{\omega}(T)^* its adjoint on {\cal H}_{\omega}. We say that T obeys detailed balance II if \pi_{\omega}(T)^* is also induced by a stochastic map. In that case we prove that \pi_{\omega}(T) is a contraction on {\cal H}_{\omega} commuting with the modular operator. The relation of this idea to microscopic reversibility, called detailed balance I, is discussed. It is shown that detailed balance II follows from detailed balance I. An entropy estimate is discussed.

REMARKS

Some further work on this topic can be found here.