  Within the Rayleigh-Helmholtz model of active Brownian particles activity is
due to a non-linear velocity dependent force. In the presence of an external
trapping potential or a constant force, the steady state of the system breaks
detailed balance producing a net entropy. Using molecular dynamics simulations,
we obtain the probability distributions of entropy production in these steady
states. The distribution functions obey detailed fluctuation theorem for
entropy production. Using simulation results, we further show that the steady
state response function obeys a modified fluctuation-dissipation relation.
