There are three major sources of the 'randomness' underlying noise phenomena. These are the random outcomes of quantum 'measurement' processes, the random ensembles of statistical mechanics, and the algorithmic complexity of many dynamical processes. Here I dwell on the possible connections between the first two sources of randomness. It is often held that the empirical irreversibility of quantum measurement arises from statistical mechanics. I present somewhat speculative arguments that in fact the irreversible approach to statistical ensembles may be rooted in an irreversible quantum decoherence process.