...but hydrogen assist can actually help. for all you car guys thinking your mechanical knowledge translates to physics, everyone seems to have overlooked one key reality of the system:
quoting the first law of thermodynamics (energy cannot be created nor destroyed) to disprove the process of getting a net-gain in fuel economy from using power from your alternator to electrolyze hydrogen out of water, is invalid because that is not what is claimed to be happening.
The question, and answer to it, is simple: How can you NOT violate the thermodynamic law? Because you're adding another fuel source. The processes don't have to be 100% efficient to see a net gain - they don't have to be anywhere near that - because the total quantity of the 'fuels' your vehicle carries and uses is increased. It is a given that putting the added strain on your alternator to electrolyze the water into hydrogen and oxygen will make your engine work harder, and thus consume more fuel. It's also a given that hydrogen will burn with gasoline in your engine, quite easily.
So long as your adding more fuel to the whole system, via the total quantity of hydrogen that gets electrolyzed from water, vs. the EXTRA amount that will be burned (probably similar to what it takes to run your air condition = negligible) you will see a net gain in efficiency. Technically, the different fuel mixture might itself burn more efficiently (which would also help compensate against the added engine strain) which would need to be incorporated into the equation, and the formula for your vehicles efficient would technically need to be modified as well - to also account for the extra water that you have to add for the HHO system to work.