Statistical Mechanics of Interacting Run-and-Tumble Bacteria

We consider self-propelled particles undergoing run-and-tumble dynamics (as exhibited by E. coli) in one dimension. Building on previous analyses at drift-diffusion level for the one-particle density, we add both interactions and noise, enabling discussion of domain formation by “self-trapping,” and other collective phenomena. Mapping onto detailed-balance systems is possible in certain cases.

Figure 1

Spinodal-like behavior of 6400 interacting particles within the region where $d^{2}f/d{\rho }^2<0$. In the numerics, $\tilde{\rho }$ is defined by convolution of $\rho$ with a smooth function of finite range $\pm 1/2$; we set $v_0=2.5$, $\lambda =0.01$, $\phi =250$. The box length is 16, with periodic boundary conditions, and the mean density is 400. Dashed lines show the common-tangent densities ($\rho =60;800$).