Langevin equations with time-correlated friction and noise are the natural equations of motion when Hamilton dynamics in high-dimensional phase space is projected on a small number of generalized coordinates. Different algorithms exist to parametrize Langevin models, and they are typically applied to study friction properties in systems that do not feature high kinetic barriers in phase space. We here adopt a different viewpoint: 1) we explicitly address high-barrier processes (rare events), 2) we employ out-of-equilibrium transition path sampling trajectories, that efficiently explore the relevant regions of phase space independently of barrier height, and 3) we optimize Langevin models with the aim of extracting accurate free energy profiles, diffusion profiles, and kinetic rates. In this way, Langevin equations become an efficient tool to obtain very rich thermodynamic and kinetic information from short unbiased path sampling trajectories.
After illustrating memory effects in relevant scientific problems (from chemical reactions in solution to protein-protein interaction) we will present a simple likelihood-maximization scheme that allows diagnosing whether a time resolution exists that allows neglecting memory effects while at the same time providing free energy landscapes and rates through the data-driven Langevin model. We show that the new approach yields accurate thermodynamic and kinetic information starting from a limited amount of path sampling data, opening the possibility of several applications to complex systems. Finally, we will briefly discuss the possibility of obtaining information of comparable quality on short timescales, where memory effects are explicitly taken into account: this is of particular relevance for chemical reactions, where transition paths are very quick.