Figure 15.

Run-and-tumble motion with diffusion on a ring $x\in [0,L)$. A run-and-tumble particle switches stochastically, in a Poisson process with rate $\alpha$, between two modes 1 and 2 characterised by an identical diffusion constant D but distinct drift velocities $v_1$ and $v_2$. The two modes are here represented in black and grey, respectively. For arbitrary positive diffusion constant D or tumbling rate $\alpha$ with $v_1\ne v_2$, the steady state is uniform but generally non-equilibrium.