Geometric approach to nonequilibrium hasty shortcuts

Complex and even non-monotonic responses to external control can be found in many thermodynamic systems. In such systems, non-equilibrium shortcuts can rapidly drive the system from an initial state to a desired final state. One example is the Mpemba effect, where pre-heating a system allows a system to cool faster. We present nonequilibrium hasty shortcuts -- externally controlled temporal protocols that rapidly steer a system from an initial steady state to a desired final steady state. The term ``hasty'' indicates that the shortcut only involves fast dynamics without relying on slow relaxations. We provide a geometric analysis of such shortcuts in the space of probability distributions by using time-scale separation and eigenmode decomposition. We further identify the necessary and sufficient condition for the existence of non-equilibrium hasty shortcuts in an arbitrary system. The geometric analysis within the probability space sheds light on the possible features of a system that can lead to hasty shortcuts, which can be classified into different categories based on their temporal pattern. We also find that the Mpemba-effect-like shortcuts only constitute a small fraction of the diverse categories of hasty shortcuts. This theory is validated and illustrated numerically in the self-assembly model inspired by viral capsid assembly processes.