The thermodynamics of stretched rubber, a function of speed?

By stretching a rubber band slowly and then slowly releasing it can we minimize the energy lost, (minimize the change in entropy?)? If so should a hysteresis curve be a function of the rate at which the rubber is deformed?

See,

http://en.wikipedia.org/wiki/Hystere...tic_hysteresis

Then should the curve in the link above state so?

Thanks for any help!