Convergence and secondary entropy in a macrodiachronic perspective

The theory of secondary convergence and entropy has had interesting results in the comparative linguistics of Semitic languages, as in the studies of Lutz Edzard who analyzed the secondary convergence between various Semitic languages once they were already distinguished from one another as separate branches deriving from Proto-Semitic. However, Edzard’s contribution to the issue of secondary convergence regards only languages of the same family, the Semitic languages, a relatively small language family integrated in the loose macro-family of Chamito-Semitic (Afroasiatic) languages. What should be expected now is the application of a similar methodology that could take into account the dynamic of mutual convergence between languages belonging to families looser than the Semitic languages and tighter than the Chamito-Semitic ones.My assumption is that at late stages of Proto-Indo-European (PIE) (around 2500 BC), when PIE had already been divided into various dialects, the dynamics of entropy and convergence could also have been at play between languages of different origin, not only between branches of the same linguistic family. The question is whether the contact of various subdivisions of PIE with allogenic languages could be perceived from a different perspective: not only as a centrifuge process with respect to PIE, but also as a centripetal process, by way of which initially non-IE languages were eventually Indo-Europeanized.