  We obtain within Fokker-Planck dynamics an explicit generalization of
Einstein's relation between drag, diffusion and equilibrium distribution for a
spatially homogeneous system, considering both the transverse and longitudinal
diffusion for dimension n>1. We then provide a complete characterization of
when the equilibrium distribution becomes a Boltzmann/J"uttner distribution,
and when it satisfies the more general Tsallis distribution. We apply this
analysis to recent calculations of drag and diffusion of a charm quark in a
thermal plasma, and show that only a Tsallis distribution describes the
equilibrium distribution well. We also provide a practical recipe applicable to
highly relativistic plasmas, for determining both diffusion coefficients so
that a specific equilibrium distribution will arise for a given drag
coefficient.
