CNO Cycle: 4H $\rightarrow$ He
4 protons (i.e. Hydrogen nuclei) combine to form a Helium molecule while releasing 26.7 MeV energy. This is the net result of any of the various fusion pathways for hydrogen to helium.
Three Helium molecules combine to form a Carbon molecule, while releasing 7.4 MeV of energy. Since it takes three CNO reactors (and 12 protons) to make a Carbon molecule, we now have a net gain of 87.5 MeV.
See the link, this is a long chain of reactions, each successively adding a Helium to get to a bigger element, until we get to Fe-52. The total energy released by this chain is 80.6 MeV. Taking into account the 87.5 MeV to form the initial carbon and 11 $\times$ 26.7 MeV to form all of the Helium, the net energy gain from fusion is 462 MeV, divided by 52 initial protons.
Now, Fe-52 is not the most stable element, and you could theoretically get more energy by reacting up to Fe-56 or Ni-62 or something. But, I wasn't able to find a clear path for fusion up to that point. In the real world, creation of these elements is a result of an equilibrium between various fusion reactions and photodisintegration and such. I think this energy estimate is the best for your purposes.
Energy released by accretion
This is much more difficult to estimate, because there are a lot of factors here, and it depends strongly on the size of your black hole and shape of the accretion disk. However, reworking an estimate of luminosity based on mass transfer rate into a black hole gives:
$$E = \frac{\mu m}{R},$$ where $\mu$ is the standard gravitational parameter for the black hole, $m$ is the mass of the object falling into it, and $R$ is the radius of the accretion disk.
Lets take the black hole at the center of our galaxy as an example. I calculate $\mu$ to be about $5.7\times10^{26}$ and $r$ about $7.5\times10^{12}$ meters (~ 50 AU). Therefore, each AMU generates about 0.8 MeV as it falls into the accretion disk. Consider this a pretty rough estimate. The problem here is that much of this kinetic energy is either a. carried into the event horizon by the falling particle or b. radiated into the event horizon by the accretion disk. Either way, much of the released energy is unusable.
Conclusion
You get about 9 MeV from fusion per AMU of protons that you throw into this process, and less than 0.8 MeV from accretion per AMU of protons. Converting to J and kg, we get 870 TJ per kg from fusion, and less than 77 TJ per kg from accretion. So, you are looking at something in the range of 900 TJ per kg of hydrogen.
Once there is no energy gradiant left to exploit entropys final order will purge the universe of all life. Only stored data will remain in skeletally stripped down storage facilities.
Not really, maximum entropy means there will be no persistent gradient anywhere, so your data will be gone with the rest $\endgroup$