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

Picture a lake that embodies energy equilibrium. Anything heavier above the lake falls, and anything light below the water level raises.
Opposite directions, they both produce movement.