[Nextgrid]

Technically a "perfect" miner would use zero energy (beyond microamps for driving the signal wires in the network cables), the heat comes from imperfect components that "waste" energy by turning it into heat.

So the mining itself doesn't use any energy, it's just that instead of dumping power into a dumb coil of wire, you dump it into a smarter coil of wires and various components that produce some output (that happens to be valuable to the Bitcoin network and it rewards you in exchange) as a side-effect.

For any given watt of electricity, the heat output is the same, just that with a miner you also get useful calculation results out of it.

[elseless]

The Landauer principle states that any computation involving information erasure (e.g., taking the hash of blocks) must correspond to some nonzero increase in entropy, which would be expressed here as heat.

[Empf]

That's not possible. Physically speaking

[jwalton]

It definitely is.

Heat is the most retrograde form of energy - the form with the most entropy. You can put 100W into a resistor, and you’ll get out 100W of heat. You can put 100W into a lightbulb, and it will generate less than 100W of light and some heat (because it’s not perfectly efficient) but in a room with no windows that light will bounce around until it’s absorbed by the walls and turned into heat so the room will heat up the same as if you had a 100W heater. If you put 100W into a miner, it will mine bitcoins and shed 100W of heat.

Water always runs downhill, energy always follows entropy down into heat.

Edit: Maybe this example will make more sense - consider an old fashioned record player. If the turntable is magnetically levitated, and is in a vacuum chamber, you can spend a tiny amount of energy to spin the table up to 45 rpm, and then (with no needle on the record) it will spin at that speed basically forever, because it's in a frictionless environment (there's no real frictionless environment, of course - you'll need a tiny amount of energy to keep it going). If you have an old turntable from the 70s where all the cheap grease has hardened, then to keep it spinning, the motor will have to do some work. Let's say you're putting 5W in to keep it turning. That 5W is overcoming the friction from the air, and from the old grease, and from the belt drive that runs the turn table. That friction is generating 5W of heat. It has to be, because if it was generating less than 5W of heat then either we'd be using less than 5W to maintain a steady state, or the else the turntable would be accelerating until we were using 5W to maintain a steady state.