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Probably not, as all matter has an energy component associated with it, even when it is at apparent rest.

For example, a 1kg rock at Earth's equator is really moving at about 40 000 km/day; and if we consider the motions of the Solar system, and of our Galaxy, then the energy of that apparently stationary rock is quite great.

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Q: Is it possible at least theoretically to have a system which allows the transfer of matter but not energy?
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