There needs to be a gradient or the wax won't move due to temperature. The motion is the change in state, as you say, but it won't change state if you don't heat or cool it.
replyThat's why it's a motor, like in dishwashers, not a thermostat like in e.g. greenhouse windows or radiators.
It doesn't need to be persistent, but without some way to create a state that is different than ambient, it's not a motor.
I disagree, I think motor in this case only means “creating movement”. The motor is the thing creating movement depending on the ambient temperature.
replyAlso you seem to have a miscommunication with the person replying to where they are talking about a special thermal gradient and you mean it in a temporal sense.
The wax expands due to ambient (even uniform) temperature. It's a linear actuator, so warm -> expanded and cool -> retracted.
replyI think by thermal gradient they mean a change in temperature over time, not space.
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