How would you experimentally realise mechanism 1? It still feels like you need an additional mechanism to capture the energy, and it doesn’t necessarily seems easier to experimentally realise.
One example (probably not the easiest thing to implement in practice) is the charge-patterned wheel that I mentioned in my thread with Jacob. If we’re lowing the energy of a state while the particle is in that state, then the potential gradient puts a force on the particle which pulls back on the wheel, increasing its energy.
With regards to 2, you don’t necessarily need a thermal bath to jump states, right? You can just emit a photon or something.
If you’re emitting into vacuum (no other photons there at all), then that’s like having access to a thermal bath of temperature 0. Erasure can be done for arbitrarily low cost under such conditions. If the vacuum has temperature higher than 0, then it has some photons in it and occasionally one of them will come along and knock into our particle. So then we pretty much have a thermal bath again.
One example (probably not the easiest thing to implement in practice) is the charge-patterned wheel that I mentioned in my thread with Jacob. If we’re lowing the energy of a state while the particle is in that state, then the potential gradient puts a force on the particle which pulls back on the wheel, increasing its energy.
If you’re emitting into vacuum (no other photons there at all), then that’s like having access to a thermal bath of temperature 0. Erasure can be done for arbitrarily low cost under such conditions. If the vacuum has temperature higher than 0, then it has some photons in it and occasionally one of them will come along and knock into our particle. So then we pretty much have a thermal bath again.