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Compressing neon gas won't do much, aside storing energy as compressed fluid.

My point was the traditional fuels (incl. the edible ones) use more material/weight than their own. So it is very likely they'll be more efficient. The batteries require a reversible action by just applying current - this is quite the climb compared to most chemical reactions.

We have not done much since the li-ion inception, using FePO4 instead of cobalt is more sensible from an economic point of view but the energy density is even lower.