( This is a topic I know almost nothing about,  so I don't know the correct units for measuring electricity and hydrogen in this topic  )

First,

- Say you use 5-units of electricity for 1 minute,  to produce 1/2-litre of hydrogen

- Then, you use the absolute smallest spark possible to ignite the 1/2-litre of hydrogen

- NOW,   if it was possible to use the energy from the explosion of the 1/2-litre of hydrogen,   to produce 'More' than  1/2-litre of hydrogen( via any method ),  then you could achieve overunity .

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      So,  to use the explosion of the 1/2-litre of hydrogen to try and produce 'More'  than 1/2-litre of hydrogen,  here are 2 possible methods :
       -   I recently read that they have invented a camera that just uses the energy received by it's image sensor,  to power the whole camera,  and also,   extremely sensitive infrared-cameras have  existed for a some time.  So,  could an explosion chamber lined with these materials, convert enough of the energy from the explosion, into electricity,  remembering that heat is mostly in the infrared range
( I'm assuming that part of the electromagnetic wavelengths( frequency ) of the explosion,  could not be converted to electricity by these image-sensor materials,  and I don't know the electromagnetic frequency ranges of solar cells  )

       -  Or,  could you use the burning/exploding hydrogen,  rising( floating)  up through another container of water,  to generate more hydrogen( or other some other usefull gas ),  this is an idea I cannot expand upon,  since I know nothing about chemistry .

Other than using graphene,  or the latest inventions of the very ultralight foams and gels ( made of metals ) to produce the tiny current to produce hydrogen through electrolysis,   I always had the idea of the old photo-etched semiconductor chip processes,  that one of those old memory chips,  could( possibly without having all it's coatings ) provide enough electrical contacts per square-mm to increase the efficiency of  electrolysis,  and you could put these plates facing each other .

Burning to make electricity in any known way is not efficient. A fuel cell might be better. Platinized platinum is one of the better electrodes as it has a low over potential. Look up different materials for their hydrogen and oxygen overpotentials. As far as browns gas being special, don't believe it. Monoatomic oxygen and hydrogen are unstable. They would quickly recombine to form diatomic molecules especially on metallic surface spontaneously. In doing so a large amount of heat would be given out. This has not been shown to occur.

I know very little about electrolysis and chemistry .

Yes, logically,  the more solid-state that a device is,  or more like a chemical-battery it is,  then it should be more efficient .

That made me realize, that molds/plants/insects etc must be very efficient in some ways.  I assume overunity cannot exist,  but I wonder how close to overunity nature can get .

Maybe copying living things could produce the most efficient batteries or generators

The wikipedia article quotes the efficiency as MJ per cubic metre of HYDROGEN ,not the volume of the evolved gases. You'll  discover there is no overunity using your claimed figures.