Quantum tunneling increases the rate of energetically favorable reactions, but it can't create energy from nowhere. Eg. in the muon catalysis case, the reaction

Quantum tunneling increases the rate of energetically favorable reactions, but it can't create energy from nowhere. Eg. in the muon catalysis case, the reaction (D + T -> He4 + H) produced a huge amount of energy as soon as nuclei could "tunnel through" the barrier. In this case (p + e -> n + v), no energy is produced even after the barrier is overcome; the energy used to overcome the Coulomb barrier goes into the mass of the neutron. Hence, that energy still must come from somewhere.