  We take up the question why the initial entropy in the universe was small, in
the context of evolution of the entropy of a classical system. We note that
coarse-graining is a an important aspect of entropy evaluation which can
reverse the direction of the increase in entropy, i.e., the direction of
thermodynamic arrow of time. Then we investigate the role of decoherence in the
selection of coarse-graining and explain how to compute entropy for a decohered
classical system. Finally, we argue that the requirement of low initial entropy
imposes constraints on the decoherence process.
