  We derive the exact relation for the energy transfer in three-dimensional
compressible two-fluid plasma turbulence. In the long-time limit, we obtain an
exact law which expresses the scale-to-scale average energy flux rate in terms
of two point increments of the fluid variables of each species, electric and
magnetic field and current density, and puts a strong constraint on the
turbulent dynamics. The incompressible single fluid and two-fluid limits and
the compressible single fluid limit are recovered under appropriate assumption.
In the single fluid limits, analyses are done with and without neglecting the
electron mass thereby making the exact relation suitable for a broader range of
application. In the compressible two fluid regime, the total energy flux rate,
unlike the single fluid case, is found to be unaltered by the presence of a
background magnetic field. The exact relation provides a way to test whether a
range of scales in a plasma is inertial or dissipative and is essential to
understand the nonlinear nature of both space and dilute astrophysical plasmas.
