I think I'm getting the mental model. It took me a minute to get how it cycles.

I think the material reduces entropy(atomic disorder), which is transformed into heat energy. Then you take that heat and move it elsewhere, say, into some coolant. Then that heated coolant is moved away, so when the power is deactivated the material re-entropizes(?), which transforms the same amount of heat in the material back into entropy, dropping its temperature.

I think the idea then is to use one way valves to let the expanded coolant move toward a heat sink side and then allow in fresh coolant from the heat source side. It's not 'solid state' if you include the coolant system but it has definitely far fewer moving parts and far less friction than a common household heat pump.