A general way to describe a system $S$ that is entangled with an environment $E$ is
$\rho_{S}=Tr(\rho_{SE})=\sum\limits_{m,n}c_mc^*_n |s_m\rangle \langle s_n| \langle e_n|e_m\rangle$
with $\psi_S=\sum\limits_n c_n|s_n\rangle$ the state of the system and $|e_n\rangle $ the corresponding environment states.
In general the different environment states can not be considered as orthogonal, thus my question more neatly formulated is:
Is there a general mechanism, such that the environment states become orthonormal, or is this actually just a hypothesis essential for the emergence of decoherence (that has been supported by many model calculations and experiments).