Conservation of <probability> obeys $\partial_t f+\nabla_{q,p}\cdot(f\mathbf v)=0$. Expand the divergence and use incompressibility to obtain $\partial_t f+\mathbf v\cdot\nabla_{q,p}f=0$, or $\boxed{df/dt=0}$. This is fine-grained transport for <Hamiltonian> trajectories without sources or collisions. Coarse graining can obscure this constancy without contradicting it.

Solution

Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S7 / 3 / c / Solution

 Solution (source code)