Entropy production by active particles: Coupling of odd and even functions of velocity

Non-equilibrium stochastic dynamics of several active Brownian systems are modeled in terms of non-linear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for total entropy production in such systems using the Fokker-Planck equation. The result is consistent with the expression for stochastic entropy production in the reservoir, that we obtain from probabilities of time-forward and time-reversed trajectories, leading to fluctuation theorems. Numerical simulation is used to find probability distribution of entropy production, which shows good agreement with the detailed fluctuation theorem.