Decoherence, chaos, quantum-classical correspondence, and the algorithmic arrow of time

The environment -- external or internal degrees of freedom coupled to the system -- can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states: Continuous destruction of superpositions leads to environment-induced superselection (einselection). Here I investigate it in the context of quantum chaos (i. e., quantum dynamics of systems which are classically chaotic).