Adiabatically stretching a rubber band When a rubber band is stretched it heats up, but how can this be explained (from the microscopic view) in the case of an adiabatic expansion (meaning that the entropy remains constant). Further more how would we perform such an expansion because typically stretching a rubber band would straighten its molecules and decrease entropy?
 A: The answer lies in changes in Gibbs Free Energy:
$$\Delta G= \Delta H -T \Delta S,$$
where $G$ is Gibbs Free Energy, $H$ is Enthalpy, $S$ is Entropy and $T$ absolute temperature.
When we stretch the rubber band it heats up due to viscous friction of the molecules sliding over each other as we stretch the object. It as nothing to do with with adiabatic expansion because there in no expansion: rubber is an incompressible material (it deforms on stretching but $\Delta V \approx 0$).
Now we know the stretched rubber wants to snap back, so why is this? We know that this spontaneous phenomenon of snapping back means that:
$$\Delta G<0$$
We also know that on snapping back, $\Delta H<0$, so that doesn't really help.
The reason that $\Delta G<0$ is caused by an Entropy change $\Delta S$, so that for snapping back:
$$T\Delta S>\Delta H,$$
and thus for snapping back:
$$\Delta G=\Delta H-T\Delta S<0$$
This increase of Entropy when going from the stretched to the unstretched state is also easily explained from a structural molecular point of view. Rubber is made up of cross-linked macro-molecules that have a larger number of molecular conformations (micro states) when relaxed as opposed to when stretched. This translates into higher Entropy content in the relaxed state.
A: OK, sorry for the confusion, only now maybe I really understand your question. The answer is probably as simple as this: when you stretch the band, the molecules of the rubber band actually move (or fluctuate) faster. Why they move faster? You can think of a string, one end is fixed to the wall, the other is at your hand. In the middle of the string you have a mass. The mass is moving with some kinetic energy. When you stretch the string, although the space seems to be narrow for the mass to move, its kinetic energy increases because of your action of pulling the string. (This is again a mechanical adiabatic process as I wrote.)  The (kinetic) energy, and therefore the temperature increase. The entropy is logarithm of the phase volume (space x momentum), and can be shown to be actually constant, however. 
