What the GP meant is not that the distinction should be "is the abstract process carried out using electrons or chemical reactions". What he (presumably) meant, was "does the novelty lie in the abstract process, or does it lie in the physical process". Figuring out an energy-efficient way to split water into oxygen and hydrogen obviously can be represented via abstract formulas, the but the novelty does not lie in the maths but in the physical insight.
Conversely, an algorithm that performs a quicker FFT is an innovation in mathematics rather than in physics, even if when calculating that formula using a CPU uses less electricity. I.e., the fact that any kind of mathematics can be calculated using physical means (including our brains), should not suddenly render it patentable. The innovation is not a new understanding about how electrons work. And no, generally implementing that same innovation in hardware would/should/is not be patentable either (the innovation is not in how to build hardware). That why they came up with the integrated circuit layout design protection (although it's not very popular due to it being way narrower than a patent, and of course it's always more fun/interesting to have broad exclusion rights instead of narrow ones).
In general, this kind of philosophical discussion does not lead anywhere though. The easiest way to demonstrate why software patents don't work is to simply look at the negative effects of how they work in practice.