Abstract
To illustrate the plausibility and difficulties involved in problems that require a modification of the winding number notion, the author studies the statistical model of a long chain entangling with a straight rod, and calculates the statistical rate for the chain to become disentangled using the reaction rate point of view. For the measure of entanglement the usual distinction between the clockwise and the anticlockwise winding numbers is no longer applicable because, as far as the mutual snaring is concerned, only the sum of these two numbers is relevant. The author performs the calculations for the equilibrium case with a small friction and the static case with a large friction. The results are consistent with the prediction of the existing phenomenological 'tube' model for polymers.