The lack of a general framework for studying disordered systems represents a significant gap in our understanding of matter. Nevertheless, it has been proposed that the zero-temperature jamming transition of soft spheres represents an idealized starting point for understanding a variety of amorphous systems, thus playing the counterpart to the perfect crystal. While this transition effectively captures the fundamental features of an ensemble where interactions depend only on particle separation, in this talk I will explore the consequences of moving to a larger ensemble where bonds contain internal degrees of freedom. I will start by presenting a powerful new principle of disordered matter that describes how far in phase space an elastic network is from a certain mechanical response. We will then see how this can be applied, both directly and indirectly, to understand two cases where non-trivial biological-like functionality emerges in simple systems as a result of bond dynamics. This work shows the importance of considering a broader ensemble of disordered materials and lays the groundwork for understanding and developing physical processes with non-trivial structure-behavior relations