Title: Non-reciprocal multifarious self-organization

Abstract: A hallmark of living systems is the ability to employ a common set of versatile building blocks that can self-organize into a multitude of different structures, in a way that can be controlled with minimal cost. This capability can only be afforded in non-equilibrium conditions, as evident from the energy-consuming nature of the plethora of such dynamical processes. In the last three decades, synthetic self-assembly has experienced a significant boost with the development of tools to design specific interactions at different scales, from nucleic acids and peptides to proteins and colloids. To achieve automated dynamical control of such self-assembled structures and transitions between them, we need to identify the relevant fundamental aspects of non-equilibrium dynamics that can enable such processes. Here, we identify programmable non-reciprocal interactions as a potential paradigm using which such functionalities can be achieved. In particular, we propose a model that enables a system to learn and retrieve predetermined desired structures and transition between them, thus behaving as a shape-shifter. The learning rule is composed of reciprocal interactions that lead to the equilibrium assembly of the structures, and non-reciprocal interactions that give rise to non-equilibrium dynamical transitions between the structures.