Reduced Models for Motion in Fluctuating Nonequilibrium Media: Evaluating Energy Transport and Predicting Transition Rates in Steadily Driven Systems

The project RedNeq aims for powerful reduced descriptions of nonequilibrium media, including suspensions of active matter or of steadily driven particles, by benchmarking the fluctuation dynamics of test particles immersed in them. The first goal is to characterize the dynamics of these probes via extended and general Fluctuaton-Dissipation relations, which can be treated as a recipe for writing Langevin equations for probes in nonequilibrium baths. That reduced dynamical description of nonequilibria is essential for the study of at least two other classes of phenomena that are envisioned in RedNeq: (i) Energy and particle transport between nonequilibrium baths, as relevant in Physics of Life systems such as biological power houses, molecular motors and bio-engines more generally; (ii) Metastability in and around steady nonequilibria from effective nonequilibrium reaction-rate formulae, as for example important in the evaluation of dynamical large deviations, first-passage times and tipping points.The focus is theoretical and foundational for the construction of nonequilibrium statistical mechanics and soft condensed matter, with the core models, techniques, and methodologies being from stochastic processes, graph theory and path-space integration. The results of the project will be closely aligned and helpful for the ongoing biophysics ands soft matter experiments involving calorimetry and microrheology, since it will provide generalized guidlines and ready to use formulas for noise friction relations, athermal energy conductivities, and transition rates, when dealing with nonequilibrium baths.