The Fokker-Planck Equation for Active Matter

Abstract

The laws of thermodynamics of colloidal particles are well understood in equilibrium. When these colloidal particles swim by themselves, i.e. due to some chemical reaction, they are called active. Systems with active particles are not in equilibrium and the laws of thermodynamics no longer hold. Starting with the Langevin equations we derive the corresponding Fokker-Planck equation. We focus on 2 dimensional systems in the low density limit and with a low swimming speed. When we investigate the asymptotic behavior of the density of particles near a wall and the two-body correlation function, we conclude the correlation length is not universal, in contrast to equilibrium (de Carvalho and Evans, 1994).