Distribution Functions for Inertial Run‐and‐Tumble Particles in Shear‐Thinning Media

We study the dynamics of an athermal inertial run‐and‐tumble particle moving through a shear‐thinning medium in one dimension. A symmetric dichotomous noise of strength and flipping rate models the activity of the particle, while the medium's velocity‐dependent viscosity is represented by a Coulomb–tanh function, . Starting from the Fokker–Planck equations corresponding to particle's equation of motion, we analytically derive the steady‐state velocity distribution , and numerically compute the time‐dependent joint probability density function . We also solve the particle's equations of motion to obtain time‐dependent velocity and position distributions, and compare them with the marginal distributions computed from . exhibits multiple transitions as increases for a fixed , eventually approaching a Gaussian‐like profile. We identify these transition points and characterize the degree of non‐Gaussianity by computing the kurtosis.