  We reconsider the old but yet unsolved problems, origin of the universe and
the arrow of time. We show that only the closed universe is free from the
singularity with the arrow of time symmetric with respect to the maximal size
of the cosmic scale. The Wheeler-DeWitt equation is explicitly solved to obtain
the local dynamical times. Corresponding to these local dynamical times, the
thermodynamic arrow of time is proved to coincide with the arrows of dynamical
time and of expanding universe (cosmological time). The proof is explicitly
shown in two-dimensional spacetime.
