Topological entropy of a stiff ring polymer and its connection to DNA knots

Details Topological entropy of a stiff ring polymer and its connection to DNA knots Topological entropy of a stiff ring polymer and its connection to DNA knots

2001-03-07

arxiv.org/abs/cond-mat/0103156v1

Physics

Condensed Matter

Statistical Mechanics

14pages,11figures

Scientific paper

10.1143/JPSJ.70.1523

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.

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