  Plasmas in an accretion flow are heated by MHD turbulence generated through
the magneto-rotational instability. The viscous stress driving the accretion is
intimately connected to the microscopic processes of turbulence dissipation. We
show that, in a few well-observed black hole accretion systems, there is
compelling observational evidence of efficient electron heating by turbulence
or collective plasma effects in low accretion states, when Coulomb collisions
are not efficient enough to establish a thermal equilibrium between electrons
and ions at small radii. However, charged particles reach a thermal equilibrium
with their kind much faster than with others through Coulomb collisions, a
two-temperature accretion flow is expected. We consider a Keplerian accretion
flow with a constant mass accretion rate in the pseudo-Newtonian gravitational
potential and take into account the bremsstrahlung, synchrotron, and inverse
Comptonization cooling processes. The critical mass accretion rate, below which
the two-temperature solution may exist, is determined by the cooling processes
and the collisional energy exchanges between electrons and ions and has very
weak dependence on the collision-less heating of electrons by turbulence, which
becomes more important at lower accretion rates. Collision-less heating of
electrons by MHD turbulence can no longer be ignored in quantitative
investigations of these systems.
