Entropy of a polymer contained in a sphere with infinitely thin chords 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?
 A: All states are accessible
Basic assumption of statistical physics is that all "allowed" configurations are equally probable. And the entropy is related to the number of those configurations. Therefore entropy won't  change if all the configurations would be still accessible after introduction of the chords. Which is the case if length of joints of your polymer are much smaller than the characteristic length of/between the chords in the volume.
Of course even in this case the chords will affect the diffusion times. The configuration space will have some complex structure with interconnected "islands", which must have some relation to glasses. But the total number of states and, therefore, the entropy won't change. 
Inaccessible states
If length of joints becomes comparable to the size of the sphere and/or characteristic length of/between the chords, then the "chordless" configuration space will be broken in several mutually inaccessible subspaces. 
I think one can imagine an example when the number of those subspaces equal to the number of
"stamp foldings". And as far as I know this combinatorial problem is yet unsolved -- not only there is no closed expression, but not even guesses about the asymptotic behaviour (here).
