Entropic force in polymers

According to my textbook, the elastic force in a rubber is caused to the tendency of the polymers to return to their initial disordered state of higher entropy.

But isn’t this looking at entropy on a larger level (I’m hesitant to say macroscopic) than it is usually looked at? Generally, we consider the entropy of individual atoms in an ordered structure (a crystal lattice, for instance). But here, we are looking at the entropy of entire polymer chains.

Also, it just doesn’t seem to make sense with the non-statistical view of entropy. The book explains it in the following way. The first law of thermodynamics,

$$dE = dQ – dW$$

Making some substitutions,

$$dE = TdS + Fdx$$

where $F$ is the elastic force, $dx$ is the displacement, $T$ is the temperature and $dS$ is the entropy change. Next, approximating $dE$ as zero, and solving for $F$,

$$F = -Tfrac{dS}{dx}$$

which is supposed to tell us the that the force is proportional to the rate $dS/dx$ at which the rubber band’s entropy changes. But how is there any chage in entropy when no heat is being added?

And, for that matter, if I take a string, lying all entangled, and try to straighten it, why doesn’t it exert an entropic force and try to go back to its higher entropic state?