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The high energy density of a matter/antimatter system is well known. However, depending on the nature of the material, most of the energy from the interaction is released in the form of photons (gamma rays), which are difficult to extract work from.

Is there a theory that describes the maximum amount of usable work extractable from a matter/antimatter system — something akin to the equations for calculating the maximum efficiency of a Carnot engine?

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    $\begingroup$ Since we know the total energy of an electron-positron pair and the wavelength of the photons emitted from their annihilation, the only question left is "how efficient is your capture method?" There's no theoretical upper limit to that, as far as I know, only practical upper limits - which makes it engineering, not physics. $\endgroup$ – Asher Jun 23 '16 at 20:05
  • $\begingroup$ Since the photons in the rest systems are mono-energetic, there is no thermodynamic limit for the conversion from the annihilation. That only applies to systems that have a thermodynamic temperature. The other way around, i.e. the synthesis of antimatter is severely limited, though, by the impossibility to force the impact parameter in collisions to a fixed value. $\endgroup$ – CuriousOne Jun 23 '16 at 21:20
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There was a lot of hype $10$ to $15$ years ago over the hydrogen economy. It was of course rather odd that anyone could take this seriously. How much free hydrogen gas is available? Answer: virtually none. The problem is that you have to either put electrical energy into water to split it into $H_2$ and $O_2$, or if you chemically condition methane $CH_4$ you may strip the hydrogen atoms free of the carbon, but you still have that carbon. As a result hydrogen is either an energy storage system, or a way of banking another form of energy (fossil fuels etc) in a way that lacks the carbon.

Antimatter is a similar issue, though at much higher energy. There is no freely available antimatter in the universe, at least as far as we know. With accelerators the amount of energy required to generate antimatter is far larger than the mass-energy contained in it. The energy utility in generating antimatter is highly negative at this point.

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