Imagine that I have a polymer (approximated as a freely diffusing, freely jointed chain with some number of subunits 'N'), and I place this polymer into a sphere of some volume 'V'. Next, I proceed to add a series of infinitely thin, immobile chords of length 'L' to the inner walls of the sphere.
Because these chords are infinitely thin, they will not change the inside volume of the sphere, but should nevertheless place certain topological and geometric constraints on the behavior of the diffusing polymer.
Can we quantify the change in entropy caused by the addition of these infinitely thin chords? For this calculation, what changes if we replaced the polymer with a monoatomic gas?