  A momentum space, mean field d-density wave (DDW) Hamiltonian is investigated
self-consistently. The pseudo-gapped(PG)state of YBCO is assumed to correspond
to the pure DDW state. A relation between thermodynamic potential of the system
and certain spectral weight functions is established. This yields an expression
for entropy in DDW state in the absence of magnetic field. The relation is
useful for deriving finite temperature thermodynamics of the system. We show
that the PG transition is a first order one and the entropy per unit cell
increases in this state. We also analyze the fermion occupancy, in the presence
of magnetic field, at the anti-nodal points of the Fermi surface to estimate
the frequency of quantum oscillations.
