  We discuss the entropy of a circular polymer under a topological constraint.
We call it the {\it topological entropy} of the polymer, in short. A ring
polymer does not change its topology (knot type) under any thermal
fluctuations. Through numerical simulations using some knot invariants, we show
that the topological entropy of a stiff ring polymer with a fixed knot is
described by a scaling formula as a function of the thickness and length of the
circular chain. The result is consistent with the viewpoint that for stiff
polymers such as DNAs, the length and diameter of the chains should play a
central role in their statistical and dynamical properties. Furthermore, we
show that the new formula extends a known theoretical formula for DNA knots.
