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 stochastic dynamics explore metastable states, whereas knowledge of the optimal paths offers deeper physical insight. Using an active Ornstein-Uhlenbeck particle, i.e., a particle driven by exponentially correlated noise, as a paradigmatic model, 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 finite-time optimal paths at non-zero energies, which can spiral around shoulders of the energy landscape, a distinct signature of the non-Markovian active dynamics.