I have been seeing in various comments references to replicators in Star Trek, occasionally arguing against various scenarios from the standpoint of energy usage - with arguments along the lines of "you might be able to replicate something that big, but the energy requirement would be astronomical."
We probably don't have any solid math explaining how this is done - however, are there any specific mentions that touch on the in-universe cost of this process?
I'd be thrilled at a canon-based answer - but here's some reasoning out:
It would depend on the nature of the feedstock - the majority of food is Carbon, Hydrogen, Oxygen and Nitrogen - but we need a lot of other trace elements, too (iron, potassium, sodium, chlorine, calcium, and more). Plus, things like glasses and plates need to be made - so we need silicon, too.
We also don't simply take in atomaceous nutrients - we need it in the form of simple sugars and more complex carbon chains (carbohydrates and fats), and proteins.
There are three possible ways the replicators use the feedstock:
all sugars, starches, fats, etc, are precomposed and simply assembled into a steak and potatoes. This means only transportation energy is required. Two problems: much like an inkjet printer can run out of one particular colour, too much ice cream can deplete sugar and fat before starches; and, things like glasses and plates rely on more crystalline or complex structures.
the feedstock is elemental and carbon chains and crystalline structures are composed individually on demand. This adds the energy of creating bonds to the transportation. Could still run out of specific elements, though.
the replicators can manipulate protons and neutrons into the specific atoms it needs to then create the molecules we need. Huge amounts of energy! But highly flexible.
Luckily, ships and bases have ridiculous amounts of energy on tap from warp cores and fusion reactors.
