In this paper, we give an information-theoretic treatment of the thermodynamic arrow of time.
We focus on a time-reversible stochastic process that does not have any
inherent temporal direction. We say a process is locally reversible
if its transition probabilities between two consecutive states are
unchanged under time reversal. We show that local reversibility is not preserved
in general when a process is mapped to another.
We show how localized temporal direction and causal relationship can emerge 
when a process is mapped to a sequence of types.