Primitive chain entropy

At first sight eqn (6.68) may seem to imply a paradoxical result since the entropy increases with decreasing L, the chain will contract to the state of L = 0 if its ends are not fixed. This argument is wrong. The collapse happens if the chain is confined in an infinitely long tube of given conformation, but does not happen in the case of a network, where the Rouse chain explores many tubes. To calculate the statistical distribution of L in the network, one has to take into account the multiplicity of the state specified by L. Let Q(L) be the number of primitive paths which have length L, then the probability that a primitive chain has a contour... 

The contribution to the free energy is not strictly linear because for each primitive path length L, the entropy of not only the ends, but of the rest of the chain in an entanglement network needs to be considered. 

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