  We consider statistical mechanical properties of the primitive chain network
(PCN) model for entangled polymers from its dynamic equations. We show that the
dynamic equation for the segment number of the PCN model does not reduce to the
standard Langevin equation which satisfies the detailed balance condition. We
propose heuristic modifications for the PCN dynamic equation for the segment
number, to make it reduce to the standard Langevin equation. We analyse some
equilibrium statistical properties of the modified PCN model, by using the
effective free energy obtained from the modified PCN dynamic equations. The PCN
effective free energy can be interpreted as the sum of the ideal Gaussian chain
free energy and the repulsive interaction energy between slip-links. By using
the single chain approximation, we calculate several distribution functions of
the PCN model. The obtained distribution functions are qualitatively different
from ones for the simple slip-link model without any direct interactions
between slip-links.
