  Irreversible behaviour is traditionally associated with open stochastic
dynamical systems, but an asymmetry in the probabilistic specification of a
closed deterministic system can similarly lead to a disparity between the
likelihoods of a particular forward and corresponding backward behaviour
starting from a specified time. Such a comparison is a test of a property
denoted obversibility, which may be quantified in terms of dissipation
production as a measure of irreversibility. We here discuss the procedure
needed to evaluate dissipation production in a simple, deterministic two-level
quantum system described by a statistical ensemble of state vectors and then
provide numerical results for illustrative situations. We consider cases that
both do and do not fulfill an Evans-Searles Fluctuation Theorem for the
dissipation production, and identify conditions for which the system will
display time-asymmetric average behaviour as it evolves.
