  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.
