  We review our approach to time and quantum dynamics based on non-critical
string theory, developing its relationship to previous work on non-equilibrium
quantum statistical mechanics and the microscopic arrow of time. We exhibit
specific non-factorizing contributions to the ${\nd S}$ matrix associated with
topological defects on the world sheet, explaining the r\^ole that the leakage
of ${W_{\infty}}$ charges plays in the loss of quantum coherence. We stress the
analogy with the quantum Hall effect, discuss the violation of $CPT$, and also
apply our approach to cosmology.
