Usefulness and limits of equilibrium mappings for confined active particles

Predicting the response of active particles to external potentials is notoriously difficult. Gaussian colored models have recently allowed some progress, including a systematic way to map an active system onto an equilibrium one. When the external potential represents hard walls, another approach exists, which tracks the dynamics along the walls. I will compare the analytical predictions of these two approaches with each other and with numerical simulations of various active particles (Gaussian colored noise, active Brownian, run-and-tumble) and discuss what they tell us about the scope of equilibrium mappings for active particles in external potentials.