  The direction of cascades in a two-dimensional model that takes electron
inertia and ion sound Larmor radius into account is studied, resulting in
analytical expressions for the absolute equilibrium states of the energy and
helicities. It is found that typically both the energy and magnetic helicity at
scales shorter than electron skin depth have direct cascade, while at large
scales the helicity has an inverse cascade as established earlier for reduced
magnetohydrodynamics (MHD). It is also found that the introduction of
gyro-effects allows for the existence of negative temperature (conjugate to
energy) states and the condensation of energy to the large scales. Comparisons
between two- and three-dimensional extended MHD models (MHD with two-fluid
effects) show qualitative agreement between the two.
