Nonequilibrium steady state for harmonically confined active particles

We study the full nonequilibrium steady-state distribution Pst(X) of the position X of a damped particle confined in a harmonic trapping potential and experiencing active noise whose correlation time τc is assumed to be very short. Typical fluctuations of X are governed by a Boltzmann distribution with an effective temperature that is found by approximating the noise as white Gaussian thermal noise. However, large deviations of X are described by a non-Boltzmann steady-state distribution. We find that, in the limit τc→0, they display the scaling behavior Pst(X)∼e-s(X)/τc, where s(X) is the large-deviation function. We obtain an expression for s(X) for a general active noise and calculate it exactly for the particular case of telegraphic (dichotomous) noise.