  We trace the development of ideas on dissipative processes in chaotic
cosmology and on minisuperspace quantum cosmology from the time Misner proposed
them to current research. We show 1) how the effect of quantum processes like
particle creation in the early universe can address the issues of the isotropy
and homogeneity of the observed universe, 2) how viewing minisuperspace as a
quantum open system can address the issue of the validity of such
approximations customarily adopted in quantum cosmology, and 3) how invoking
statistical processes like decoherence and correlation when considered together
can help to establish a theory of quantum fields in curved spacetime as the
semiclassical limit of quantum gravity. {\it Dedicated to Professor Misner on
the occasion of his sixtieth birthday, June 1992.} To appear in the Proceedings
of a Symposium on {\it Directions in General Relativity}, College Park, May
1993, Volume 1, edited by B. L. Hu, M. P. Ryan and C. V. Vishveshwara
(Cambridge University Press 1993)~~~~umdpp 93-60
