  We discuss the appearance of time-asymmetric behavior in physical processes
in cosmology and in the dynamics of the Universe itself. We begin with an
analysis of the nature and origin of irreversibility in well-known physical
processes such as dispersion, diffusion, dissipation and mixing, and make the
distinction between processes whose irreversibility arises from the stipulation
of special initial conditions, and those arising from the system's interaction
with a coarse-grained environment. We then study the irreversibility associated
with quantum fluctuations in cosmological processes like particle creation and
the `birth of the Universe'. We suggest that the backreaction effect of such
quantum processes can be understood as the manifestation of a
fluctuation-dissipation relation relating fluctuations of quantum fields to
dissipations in the dynamics of spacetime. For the same reason it is shown that
dissipation is bound to appear in the dynamics of minisuperspace cosmologies.
This provides a natural course for the emergence of a cosmological and
thermodynamic arrow of time and suggests a meaningful definition of
gravitational entropy. We conclude with a discussion on the criteria for the
choice of coarse-grainings and the stability of persistent physical structures.
Invited Talk given at the Conference on The Physical Origin of Time-Asymmetry
Huelva, Spain, Oct. 1991, Proceedings eds. J. J. Halliwell, J. Perez-Mercader
and W. H. Zurek, Cambridge University Press, 1993
