Control of Finite-Time Processes via State Variables

Controlling the dynamics of discrete-state, continuous-time systems is essential across various domains of physics and beyond, where the goal is to guide system states over time by adjusting the underlying probability currents through external control knobs. We develop a finite-time control framework that enables the steering of macrostates by varying microstate variables, under the assumption that currents are linear in the state variables. We provide criteria for the existence of solutions and explore controllability for both a subset and the full set of system states. We demonstrate the utility of our approach in thermodynamic systems governed by a master equation, where it offers a method for conservative driving by altering only the energy landscape. Additionally, we extend our formalism to cellular populations evolving under changing environments (i.e. bacteria evolving under varying drug concentrations), generalizing earlier work where these systems were directed along instantaneous equilibrium trajectories using counterdiabatic driving. In our framework, the distribution of genetic variants can be uniquely driven along arbitrary (including non-equilibrium) target paths by varying the fitness landscape.