Shortcuts to state transitions for active matter

Shortcut schemes can accelerate quasi-static processes in passive systems by adding auxiliary controls to realize swift transitions between equilibrium states. In active systems, however, inherently directed motion driven by free energy consumption continually drives the system away from equilibrium. In this work, we develop a shortcut framework to realize swift state transitions for active systems operating in the weak activity regime. An auxiliary potential is introduced to guide the system along a predefined distribution path, allowing it to reach the target state within a finite time. Considering the unavoidable energy cost of such a finite-time process, we derive a thermodynamic metric from the dissipative work, thereby inducing a Riemannian manifold on the space spanned by the control parameters. The optimal protocol with minimum dissipative work then corresponds to the geodesic path in the geometric space. We demonstrate this framework for two active systems confined in an external harmonic trap: one with attractive harmonic coupling and the other with repulsive pairwise Gaussian-core coupling. The strengths of both the external trap and the internal interactions are controllable. For the latter case, because the auxiliary potential cannot be derived analytically, we adopt a variational method to obtain an approximate auxiliary control. Compared to linear protocols, the geodesic protocols can effectively reduce dissipation.