  In this paper, we formulate statistical mechanics of the polymerized systems
in the semiclassical regime. On the corresponding polymeric symplectic
manifold, we set up a noncanonical coordinate system in which all of the
polymeric effects are summarized in the density of states. Since we show that
the polymeric effects only change the number of microstates of a statistical
system, working in this coordinate is quite reasonable from the statistical
point of view. The results show that the number of microstates decreases due to
existence of an upper bound for the momentum of the test particles in the
polymer framework. We obtain a corresponding canonical partition function by
means of the deformed density of states. By using the partition function, we
study thermodynamics of the ideal gas in the polymer framework and show that
our results are in good agreement with those that arise from the full quantum
consideration at high temperature, and they coincide with their usual
counterpart in the limit of low temperature.
