# Entropy change of a rubber band

When I stretch a rubber band, the fibers straighten out causing lesser randomness and more order. This should imply the entropy of the rubber band has decreased, but how does the entropy of the whole universe increase here? Does this mean a rubber band gets colder on stretching? I have seen an experiment where it gets hotter. Doesn't entropy of the whole universe increase only in spontaneous processes? Here I have to pull it hence its not spontaneous? In a nutshell, I'm really confused.

Let $L$ denote the length of the substance then you can always write
$$\left ( \frac{\partial T}{\partial L} \right )_{S} = - \left ( \frac{\partial T}{\partial S} \right )_{L} \left ( \frac{\partial S}{\partial L} \right )_{T}$$
The term $\left ( \frac{\partial T}{\partial S} \right )_{L}$ is always positive for being the reciprocal of the heat capacity per unit temperature. Thus $\left ( \frac{\partial T}{\partial L} \right )_{S}$ is positive or negative whether $\left ( \frac{\partial S}{\partial L} \right )_{T}$ is negative or positive. Therefore, if entropy decreases upon isothermal stretching then the temperature must increase during adiabatic stretching.