We consider simple models where particles move by a combination of diffusion and self-propulsion. We analyze -- numerically and analytically -- large deviations of time-integrated quantities, including measures of entropy production and dynamical activity . A variety of dynamical phase transitions are observed [2,3]. Some of these can be accounted for by fluctuating hydrodynamical theories, while others involve non-typical behaviour on the microscopic scale. This difference has implications for the scaling of the corresponding large-deviation rate functions.
 R. L. Jack, Eur. Phys. J. B 93, 74 (2020).
 J. Dolezal and R. L. Jack, J. Stat. Mech. (2019), 123208
 Y.-E. Keta, E. Fodor, F. van Wijland, M. E. Cates, and R. L. Jack, Phys. Rev. E 103, 022603 (2021).