Simultaneous Brownian motion of N particles in a temperature gradient

A system of N Brownian particles suspended in a nonuniform heat bath is treated as a thermodynamic system with internal degrees of freedom, in this case their velocities and coordinates. Applying the scheme of nonequilibrium thermodynamics, one then easily obtains the Fokker–Planck equation for simultaneous Brownian motion of N particles in a temperature gradient. This equation accounts for couplings in the motion as a result of hydrodynamic interactions between particles.