Thought I would throw out a few things for fun...
Water can be used as a fuel source.
#1> Fusion of the Hydrogen in each water molecule... already posted... no new idea here ... but sustained fusion reaction with a net surplus of energy is something that no one has been able to do yet ... even if they did ... it converts the Hydrogen into Helium in the process ... thus you have that much less Hydrogen on the planet ... and that much less potential water... and that much less tiny bit of mass.
#2> Water turning a water wheel as it flowed down hill via gravity ... this would be laughably tiny amounts of energy storage wh/kg... and storage is the right word to use ... as it if just storing the energy you spent lifting the water in the first place.
#3> Chemical reactions with water ... to be more accurate it is the higher energy state of the other reacting material that is potentially providing energy ... for instance if you put pure sodium into water it gives off hydrogen gas and heat ... the energy for that heat and to separate the hydrogen came from the chemical potential energy of the pure sodium... which is still laughably small amount of energy density... wh/kg... and it still takes more energy to produce the pure sodium than you get back out as heat and chemically stored as hydrogen.
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Water / Hydrogen can be used to improve the efficiency of an ICE.
#1> The so called 6 stroke engine ... where water is used to extract some useful energy from the waste heat normally pumped out of the engine via radiator and or exhaust ... application of the concept has proven to have technical difficulties for many years ... not a new idea... if they ever iron out all the issues ... great ... but don't hold your breath.
#2> The Hydrogen has a very fast flame speed ... and it can be used in an engine in order to support more efficient lean burn operations ... we don't see this used because there are better more efficient ways of supporting lean burn ... including things like Honda did in the Gen-I Insight including swirl effects, special spark plugs , etc... the net result is that Honda was able to support lean burn more efficiently without water or hydrogen than it could have with it.... and it didn't require them to have the customer remember to fill up tanks of water or hydrogen to let the lean burn function work.
#3> Hydrogen as a fuel source can operate the ICE itself more efficiently than gasoline can ... however you would first have to get the hydrogen in the first place ... this is just a Hydrogen powered ICE ... given the energy cost to produce the hydrogen and the low efficiencies of ICEs ... it is a efficiency dead end ... you would be further ahead to use the same produced hydrogen in a fuel cell car ... and you would be further ahead of that to use the energy you used to produce the hydrogen to just charge up a BEV.
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Produce more energy than you put in.
Under some conditions electrolysis is endothermic ... so some of the energy chemically stored in the resulting hydrogen came from ambient heat in the environment... your electrolyzer did not have to 'pay' for all of it ... the problem with this is that the amounts are too tiny ... and the efficiency levels needed to make it work ... just don't exist ... and might never exist... even if you could ( and you can't ) reach 100% efficiency in every step, including room temperature super conductive wires ... etc... the maximum potential is 14 wh per mole of water ... but remember this is not energy stored in the water ... it is converting ambient thermal energy into a different form... even at 100% efficient energy conversions 14 wh per mole with each mole being ~18g is a maximum ( magic ) potential of ~777 Wh / kg ... and gasoline contains ~13,000 wh / kg ... it would still be a tiny ~6% of the potential from the same volume of gasoline.
It works out so that the entire process must be a net of over ~82.3% efficient in order to effectively be extracting energy from the ambient heat of the room ...
The most efficient ICE I know of is just over 50% peak efficiency ... no where near enough to make the above work ... even the Honda FCX Clarity with a state of the art Fuel cells stack only converts ~60% of the energy content of the hydrogen into electricity ... which is still not good enough.
For example ... say we had some magical electrolyzer that operated at ~95% efficiency ( it's magic ) ... and we had some magical fuel cell operating at ~95% efficiency ( it's magic ) ... providing electricity to a ~95% efficient motor controller ... for a ~95% efficient Electric Motor ... and ~99% efficient Transmission... the result would be a net operating efficiency of ~80.6% ... still not good enough ... even with 'magic' components that are way better than what we have today.
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Now if we took a step away from and just forget about water or hydrogen for that mater ... the idea of operating a heat pump is more plausible ... you can move more thermal energy from point A to point B than you used to move it... this is why heat pumps can be very efficient... but is also a potential way to extract some of the ambient thermal energy.
A COP of 1.0 means for every 1.0 unit of energy put in the heat pump moves 1.0 unit of heat energy from point A to point B.
COP * 3.413 = EER
a EER of 20 = COP of ~5.8 ... or for every 1 unit of energy used by the EER 20 Heat Pump ~5.8 units of heat energy are moved from point A to point B.
with two such heat pumps one cooling a surface and the other heating it... you can create a temperature difference ... this temperature difference could then be used to power a heat engine like a Sterling ... or a thermo electric solid state module.
In order to net ambient energy extraction the heat engine or thermo-electric device at the center of the temperature difference must operate at an efficiency above inverse of the COP ... so using a ~5.8 COP heat pump would require using more than a ~17.24% efficient heat engine or thermo-electric device ... which is still no small / or easy thing ... but is at least I think more plausible.
Might be best to exploit natural temperature difference as well such as those bellow ground being at a different temperature than above ground for most of the year ... in the winter it is warmer , in the summer it is cooler... the largest temperature difference for the least energy input , makes it work best.
Of course ... sense the source of most ambient heat is sun light ... it would be much simpler and far more efficient to just convert the sun light into electrical energy , and forget about heat extracting energy second hand from ambient heat.