Energy cost of bitcoin vs physical currency?
The most extensive research on this topic is:&quot;An Order-of-Magnitude Estimate of the Relative Sustainability of the Bitcoin Network&quot; by Hass McCook
among others, it cover specific topic as the economic and environmental cost of cash printing &amp; coin minting, banking system, gold mining &amp; recycling etc ...
The results of the research are summarized in the tables below.

take in mind that these data are from 2014, so Bitcoin cost of production and consumption are actually much higher.

These are the estimation about miners efficiency at the time, when the network hashrate was 130 Phash/s and the most efficient miner was Antminer S3 with 0.766 w/Ghash:

I redid the calculations using current hashrate of 186 Ehash/s, an efficiency of miners ranging from 0.1 w/Gh of Antminer S9 to S19 0.03 w/Gh and keeping all other assumptions the same, these are the results:

About 70/80 times more consumption than was in 2014 (depending on which energy efficiency you pick as network average). Certainly the costs of the other activities (banking, mining, minting) have also increased, but not in this size.
Although the research in question is detailed, the author was honest in saying that the data is not an accurate representation of reality, but an estimate of its order of magnitude.