For the Boltzman equation, why is df/dt=0 when collisionless?

[TimeRip496]

From wikipedia,
The general equation is $$\frac{df}{dt} = (\frac{∂f}{∂t})_{force}+(\frac{∂f}{∂t})_{diff}+(\frac{∂f}{∂t})_{coll}$$
where the "force" term external force, the "diff" term represents the diffusion of particles, and "coll" is the collision term.

So shouldn't be df/dt=0 when it is not just collisionless but also force and diffusion are zero too?

Wikipedia also mention that since collisions do occur, the particle density in the phase-space volume d³rd³p changes. So will df/dt be non-zero when d³rd³p changes?
In that case for df/dt=0 without having a zero external force and diffusion, the external force and diffusion must be the same for all the particles in order to mantain the same density, am I right to say this?

 

[gtoguy97]

Yes, df/dt can be zero without having a zero external force and diffusion if the external force and diffusion are the same for all particles in order to maintain the same density. In this case, the collisions will not change the density of the system, and the equation of motion can be written as:df/dt = (∂f/∂t)_force + (∂f/∂t)_diff + 0where the "force" term represents the external force, the "diff" term represents the diffusion of particles, and the 0 term represents the absence of collisions.