  We find the hydrodynamic equations of a system of particles constrained to be
in the lowest Landau level. We interpret the hydrodynamic theory as a
Hamiltonian system with the Poisson brackets between the hydrodynamic variables
determined from the noncommutativity of space. We argue that the most general
hydrodynamic theory can be obtained from this Hamiltonian system by allowing
the Righi-Leduc coefficient to be an arbitrary function of thermodynamic
variables. We compute the Righi-Leduc coefficients at high temperatures and
show that it satisfies the requirements of particle-hole symmetry, which we
outline.
