  We establish a conceptual framework for the identification and the
characterization of induced interactions in binary mixtures and reveal their
intricate relation to entanglement between the components or species of the
mixture. Exploiting an expansion in terms of the strength of the entanglement
among the two species, enables us to deduce an effective single-species
description. In this way, we naturally incorporate the mutual feedback of the
species and obtain induced interactions for both species which are effectively
present among the particles of same type. Importantly, our approach
incorporates few-body and inhomogeneous systems extending the scope of induced
interactions where two particles interact via a bosonic bath-type environment.
Employing the example of a one-dimensional spin-polarized ultracold Bose-Fermi
mixture, we obtain induced Bose-Bose and Fermi-Fermi interactions with
short-range attraction and long-range repulsion. With this, we show how beyond
species mean-field physics visible in the two-body correlation functions can be
understood via the induced interactions.
