It's the process called 'decoherence' - which basically means the evolution of the hitherto 2-variable wave function into a multi-variable wave function which now also includes further variables from the environment . Decoherence can be partial or complete.

There are also levels of wave functions - at the very top you can argue that the universe itself has its own wave function, and that absolute full decoherence between constituents of the universe probably never takes place, although for practical purposes lower level wave functions are quite enough.

Dieter Zeh et al. have written extensively about this.

According to dilation theorems, every possible quantum evolution can be described as follows: you have a system in state rho, it interacts in a unitary way with some other initially independent system in state sigma, so that the joint system evolves to U^*(rho otimes sigma) U, where U is the unitary evolution of the joint system. Now trace out the auxiliary system to find the reduced density matrix of your original system of interest (the one which was in state rho).

Tyically it might have started being a completely entangled pure state but after the interaction (and disregarding the system it has interacted with) it is in a less entangled and typically mixed state.

There is a continuous time version of this which tells you the possible evolution of any quantum system in state rho interacting with an environment.

The process depends on the particular system-environment interaction, which can be concisely described by the channel formalism: rho_out = E ( rho_in ). The basics are nicely written in Sec. 8 of "Quantum Computation and Quantum Information" by Nielsen and Chuang (with examples of single-qubit depolarization, dephasing, amplitude-damping). Note, that you need the two-qubit channel E_12 [the simplest model is the tensor product E_1 (x) E_2 ]. Entanglement of the output state rho_out can be easily checked by the NPT criterion.

The answer this kind of problem depends explicitelly on the way your dynamical system is coupled with the environnement. You may find other insights than those quoted in the precceding messages in the books of Haken on Lasers (Springer encyclopedy of physics Fluegge ed.) and laser light dynamics where the coherence problem is carefully adressed. You have also the discussion in U. Fano Reviews of Modern Physics 1983 on "pairs of two level systems" .(U. Fano, RMP, 55, p.855, 1983