How can both nuclear fusion and nuclear fission create energy? Shouldn’t one of this action create and another consume energy according to thermodynamics laws?

Question

In a hypothetical isolated system, you could have nuclear fusion reactor and nuclear fission reactor both generating energy. Fusion reactor combining small atoms creating larger ones and fission reactor breaking these large atoms back to smaller atoms, both actions creating energy.

I know that this would be perpetuum mobile, thus it is not possible. I just struggle to understand why.

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Edit: Thank you all for explanations! Finally, it makes sense to me.

In: Physics

Answer 1

The atoms which give you a net gain from fusion give you a net loss from fission. And atoms that give you a net gain from fission would give you a net loss from fusion.

Things are a mite bit complicated but the point is, the best case scenario for your hypothetical system is a that the energy gain/loss cancel out.