Partial Entropy production of active particles with hidden states in potentials

Partially observed stochastic systems can appear (almost) time-reversal symmetric while in fact operating far from equilibrium. The present work extends the perturbative framework introduced in [Phys. Rev. Lett. 136, 198302 (2026)] to calculate in a generic confining potential the partial entropy production, which quantifies the time-reversal asymmetry of a generic active particle with hidden self-propulsion. Focusing on the harmonic case, we apply our framework to reproduce an exact result for the partial entropy production rate of an active Ornstein-Uhlenbeck particle and to derive the partial entropy production rate of a run-and-tumble particle.