Resets allow for canalization in high-dimensional state spaces

Resets have been shown to be a broadly relevant strategy for speeding up search in a broad range of contexts. Our work points out that in addition to saving time, reset mechanisms effectively reduce the entropy of paths used to reach a destination state. Such canalization into a few paths can be seen as a non-equilibrium version of Waddington's homeorhesis. The reduction in trajectory entropy can show up as higher order that can be observed in e.g. assembled structures or copied polymers. As a consequence, complex systems can achieve stereotyped reproducible behaviors, despite living in high-dimensional disordered state spaces, through simple non-equilibrium mechanisms that also provide speed benefits. We set out the minimal conditions needed for the evolution of such mechanism in an abstract model of cell division with a high-dimensional space of possible paths.