  Stochastically switching force terms appear frequently in models of
biological systems under the action of active agents such as proteins. The
interaction of switching force and Brownian motion can create an "effective
thermal equilibrium" even though the system does not obey a potential function.
In order to extend the field of energy landscape analysis to understand
stability and transitions in switching systems, we derive the quasipotential
that defines this effective equilibrium for a general overdamped Langevin
system with a force switching according to a continuous-time Markov chain
process. Combined with the string method for computing most-probable transition
paths, we apply our method to an idealized system and show the appearance of
previously unreported numerical challenges. We present modifications to the
algorithms to overcome these challenges, and show validity by demonstrating
agreement between our computed quasipotential barrier and asymptotic Monte
Carlo transition times in the system.
