Electricity is still thermodynamically degraded, irrespective of source. If Japan's electricity was 100% powered by nuclear energy it might be worthy of consideration, but it isn't.
Electrolysis further degrades the thermodynamics of electricity to store it as hydrogen, destroying more exergy.
It would be wiser to use any electricity devoted to electrolysis to the grid.
In a thermochemical cycle, the best of which, in my view, is one of the earliest considered, the sulfur iodine cycle, (SI cycle) because it is amenable to continuous flow chemistry, heat energy currently released into the environment (nuclear energy's most problematic external cost) would be recovered by exergy, and the cooling steps involved in cooling the SO2/O2 hot gas stream to prevent reoxidation might be utilized to generate electricity as a side product. If the side product electricity is available to a 100% nuclear grid, electrolysis might be marginally acceptable.
This approach is called "process intensification." Process intensification is the best industrial scale approach to sustainability there is in my view.
I believe China is testing a nuclear powered SI cycle, but I don't have an update on the status.
Thanks for your question.
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