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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 ringpolymer does not change its topology (knot type) under any thermalfluctuations. Through numerical simulations using some knot invariants, we showthat the topological entropy of a stiff ring polymer with a fixed knot isdescribed by a scaling formula as a function of the thickness and length of thecircular chain. The result is consistent with the viewpoint that for stiffpolymers such as DNAs, the length and diameter of the chains should play acentral role in their statistical and dynamical properties. Furthermore, weshow that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure

Topological Entropy of a Stiff Ring Polymer and Its Connection to DNA Knots