Geometric phase distributions for open quantum systems
  In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the environment and its coupling with the system yields a unique geometric phase distribution that applies even for mixed states, non-unitary dynamics, and non-cyclic evolutions. 
K.-P. Marzlin, S. Ghose, and B.C. Sanders