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 coarsegraining is 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 coarsegraining 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.
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