Since it is difficult to simulate the quantum dynamics of large, complex many-body systems, one is led to construct a statistical mechanical description of matter based on a mixture of quantum and classical dynamics. Many physically interesting systems may be partitioned into subsystems where certain degrees of freedom must necessarily be treated quantum mechanically, while others behave classically to a high degree of accuracy. Examples of systems with these characteristics are familiar and include proton and electron transfer processes and systems with electronic degrees of freedom coupled to heavy nuclei. In these cases it is useful to construct a quantum-classical dynamics that not only accounts for the quantum and classical dynamics of the two isolated subsystems but also describes their interaction. [1,2,3] The most widely used approaches are based on surface-hopping schemes where the coupling between the two subsystems induces quantum transitions. [4,5,6,7]