  In the Hamiltonian treatment of purely mechanical systems, the canonical and
actual momentum of a particle are the same. In contrast, for a plasma of
charged particles and electromagnetic fields, those two momenta are different.
We show how this distinction is fundamental in identifying the limitations of a
recent attempt by Binney (2003) to rule out two-temperature collisionless
astrophysical accretion flows from Hamiltonian theory. This illustrates the
Hamiltonian method for astrophysical plasmas, its relation to the equations of
motion, and its role in practical calculations. We also discuss how the
complete Hamiltonian treatment of a plasma should couple the particle motion to
a fully dynamical treatment of the electromagnetic fields. Our results stand
independent from the discussion of Quataert (2003) who argued that time scale
calculated in Binney (2003) is not the equipartition time as claimed.
