  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.

Statistical Mechanics;Soft Condensed Matter;Subcellular Processes