  Why is it that a ticking clock typically becomes less accurate when subject
to outside noise but rarely the reverse? Here, we formalize this phenomenon by
introducing process causal asymmetry - a fundamental difference in the amount
of past information an autonomous agent must track to transform one stochastic
process to another over an agent that transforms in the opposite direction. We
then illustrate that this asymmetry can paradoxically be reversed when agents
possess a quantum memory. Thus, the spontaneous direction in which processes
get 'simpler' may be different, depending on whether quantum information
processing is allowed or not.
