Averaged Kauffman Invariant and Quasi-Knot Concept for Linear Polymers

We propose the description of the qualitative idea of quasi-knot for linear open polymers in terms of averaged Kauffman state invariant, which, in turn, can be represented as a partition function of the 2D Potts model with annealed disorder. The qualitative characteristic of quasi-knot complexity is defined and is shown to be a drastically increasing function of the compactness of the 3D chain fold.