Me: OK, but if we have the long-since-amortized state-of-the-art diffusion model and if we had devices that work at the Landauer limit, then we’d have a rather remarkable piepline.

I feel like there’s something “better” in a thermodynamic sense about doing Landauer work to reach the interesting image manifold than to do the Landauer work to reach a set-up that’s got the same information entropy but is some random choice from that low-entropy subset. You’ve seen Autechre’s Gantz Graf video. Sure, it’s low entropy, but…

o3: Landauer cares only about “how many bits are written-then-forgotten,” never about what the bits denote. Two pictures that each end up as, say, a 512 x 512 x 24-bit PNG have the same minimum erase cost kT ln 2 x 512 x 512 x 24 = 2e-7 ergs whether one is a Rembrandt and the other a glitch mosaic.

Where a theromodynamic gap can appear is in the path you take:

1. Direct random fill
   • write 24 bits per pixel of fresh IID noise, keep none of them -> must eventually erase the full N = 6.3 Mbits.
   • Landauer floor: kT ln 2 N.
2. Compressed-latent generator (ideal)
   • draw m << N random bits for a latent z that indexes the learned manifold;
   • reversibly expand z|->x (keep all intermediates or uncompute them).
   • only m bits of randomness ever need to be forgotten.
   • Landauer floor: kT ln 2 m.
   • If natural images have Shannon entropy ~ 2 bpp, then m ~ 2/24 N ~ 0.08N.
3. Diffusion sampler (real models)
   • Inject fresh Gaussian noise for every pixel at every step (often > 10^8 bits total).
   • Most of those are thrown away; unless you store and later return them, the erase budget ballons, making diffusion far from Landauer optimal.

So “interesting low-entropy images” are not cheaper because they’re meaningful; they are cheaper only if you generate them through a low-entropy latent code and do the expansion reversibly. Current diffusion pipelines don’t, but a future, fully reversible lanent-decoder running at the Landauer limit could, in principle, turn a handful of random bits plus a lot of conservative logic into arbitrarily many remarkable frames with minimal heat.

Me: So ultimately it costs less to generate the good stuff than to show static on a dead television?

o3: In principle, yes.

Landauer budget = “bits created and later forgotten”.

o Dead-channel static

— you must draw a fresh random value for every output pixel -> ~ N = H x W x 24 random bits.

— those bits are discarded after use

— irreducible heat: E = kT ln 2 N.

o “Good” image via a trained generator

— draw only m << N random bits for a latent code z

— expand z -> image with reversible logic, uncomputing scratch states

— forgotten bits = m

— irreducible heat: E = kT ln 2 m.

So, with ideal reversible hardware the minimal energy is proportional to the entropy you inject, not the picture’s final file size. Because natural images are highly compressible (m/N ~ 0.1 or less) generating meaningful content can, in theory, cost an order-of-magnitude less heat than producing television snow.

Me: static.