Exact Hamiltonian Dynamics of Rare Events in Active Matter
Active systems navigate complex environments through non-equilibrium fluctuations, rendering standard equilibrium transition-rate theories inadequate. Moreover, transition rates provide only partial information on how non-equilibrium dynamics explore metastable states, whereas knowledge of the optimal paths offers deeper physical insight. Using an active Ornstein-Uhlenbeck particle as a paradigmatic model, i.e., a stochastic dynamics driven by exponentially correlated noise, we establish an exact mapping of the non-Markovian optimal path onto a higher-dimensional Hamiltonian dynamical system so that, for arbitrary force fields, optimal paths can be computed systematically by solving the corresponding Hamilton equations. Tuning the conserved energy allows us to explore diverse dynamical regimes: ranging from classical instanton trajectories strictly confined to the zero-energy surface, to closed periodic orbits that emerge only at non-zero energies, representing a distinct signature of the non-Markovian active dynamics.