Self-Propulsion Symmetries Determine Entropy Production of Active Particles with Hidden States

Entropy production distinguishes equilibrium from nonequilibrium. Calculating the entropy production rate (EPR) is challenging in systems where some degrees of freedom cannot be observed. Here we introduce a perturbative framework to calculate the time irreversibility of an active particle with hidden self-propulsion, termed the "partial EPR," which provides a lower bound to the full, physical EPR. We find that the parity symmetry, P, and time reversibility, T, of the hidden variable determine the partial EPR. Nontrivial partial EPR appears at least at sixth order in the self-propulsion velocity. We apply our framework to two processes that break P- and T symmetries, respectively: an asymmetric telegraph process and diffusion with stochastic resetting.