 Quantum models of environmental decoherence are commonly thought to provide such an account (see entry on  the role of decoherence in quantum mechanics).  These typically involve the Schrödinger equation, this time applied to a system in interaction with its quantum environment. The application can show how interactions entangle the quantum states of system and environment in a way that selects a “pointer basis” in which the system’s reduced (mixed) state remains very nearly diagonal indefinitely. Somehow a particular element of this basis is supposed to be identifiable as the system’s physical state, evolving in a way that approximates classical dynamics.