  The generalized general-relativisticmagnetohydrodynamic (generalized GRMHD)
equations have been used to study specific relativistic-plasmas phenomena, such
as relativistic magnetic reconnection or wave propagation modified by non-ideal
MHD effects. However, the "Theta" term in the generalized Ohm law, which
expresses the energy exchange between two fluids composing a plasma, has yet to
be determined in these equations. In this paper, we determine the "Theta" term
based on the generalized relativistic Ohm law itself. This provides closure of
the generalized GRMHD equations, yielding a closed system of the equations of
relativistic plasma. According to this system of equations, we reveal the
characteristic scales of non-ideal MHD phenomena and clarify the applicable
condition of the ideal GRMHD equations. We evaluate the characteristic scales
of the non-ideal MHD phenomena in the M87* plasma using the Event Horizon
Telescope observational data.
