  Brown, Preston, and Singleton (BPS) produced an analytic calculation for
energy exchange processes for a weakly to moderately coupled plasma: the
electron-ion temperature equilibration rate and the charged particle stopping
power. These precise calculations are accurate to leading and next-to-leading
order in the plasma coupling parameter, and to all orders for two-body quantum
scattering within the plasma. Classical molecular dynamics can provide another
approach that can be rigorously implemented. It is therefore useful to compare
the predictions from these two methods, particularly since the former is
theoretically based and the latter numerically. An agreement would provide both
confidence in our theoretical machinery and in the reliability of the computer
simulations. The comparisons can be made cleanly in the purely classical
regime, thereby avoiding the arbitrariness associated with constructing
effective potentials to mock up quantum effects. We present here the classical
limit of the general result for the temperature equilibration rate presented in
BPS. We examine the validity of the m_electron/m_ion --> 0 limit used in BPS to
obtain a very simple analytic evaluation of the long-distance, collective
effects in the background plasma.
