According to Zurek, the emergence of a classical world from a quantum substrate could result from a long selection process that privileges the classical bases according to a principle of optimal information. We investigate the consequences of this principle in a simple case, when the system and the environment are two interacting scalar particles supposedly in a pure state. We show that then the classical regime corresponds to a situation for which the entanglement between the particles (the system and the (...) environment) disappears. We describe in which circumstances this factorisability condition is fulfilled, in the case that the particles interact via position-dependent potentials, and also describe in appendix the tools necessary for understanding our results (entanglement, Bell inequalities and so on). (shrink)