Bitcoin energy consumption depends primarily on the cost of energy and the value of the block reward, and efficiency affects neither of those.
Not sure if I understand this sentence. Isn't efficiency strictly correlated with the cost? If you find a more efficient way to calculate the hashes, it means you've found a cheaper way. If using the same amount of energy, all the miners upgraded to more efficient devices, difficulty would increase and, therefore, so would the energy required per bitcoin (AKA, energy consumption).
By "cost of energy", I mean the cost to purchase a joule of energy. In short, the energy consumption (in joules) to produce a bitcoin,
E, approaches
E ⟶ P / C
where
P is the average price of a bitcoin in $
C is the average cost of electricity in $/J
The reason that hash rate and efficiency are irrelevant is that the difficulty adjustments keep production constant, regardless of the hash rate, the amount of energy used, the efficiency of the equipment, and the amount miners are willing to spend.
However, assuming that miners (in the aggregate) are striving to be profitable, they will spend as much as they can on energy up to the value of the bitcoins they produce. So, the value of the energy consumed producing a bitcoin (
E x
C) approaches the value of the bitcoin (
P). Thus, E ⟶ P / C. Note that there are other variable costs, but energy is the biggest and it's what we are concerned about here.
If using the same amount of energy, all the miners upgraded to more efficient devices, difficulty would increase and, therefore, so would the energy required per bitcoin (AKA, energy consumption).
Small contradiction there. If using the
same amount of energy, the energy required per bitcoin would be the
same and would not increase. Note that I am assuming a time frame that includes difficulty adjustments and time for miners to add or remove equipment. An increase in efficiency would reduce energy consumption at least until the next difficulty adjustment, but consumption would return as miners compete for a bigger share.