Due to the 2nd law of thermodynamics, it is impossible to convert anything to energy and back without extra energy as input. So this hypothetical arrangement can't happen.
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Basically it's a matter of quotation units.
One energy coin can be exchanged for one joule, but it takes more than one joule to be mined, or one joule is mined for one energy coin, only to convert to less than one.
Each energy coin must definitely be converted to the same amount of energy.