If you read landauers paper carefully he analyzes 3 sources of noise and kTlog2 is something like the speed of light for bit energy , only achieved at useless 50% error rate and or glacial speeds.
That’s only for the double well model, though, and only for erasing by lifting up one of the wells. I didn’t see a similar theorem proven for a general system. So the crucial question is whether it’s still true in general. I’ll get back to you eventually on that, I’m still working through the math. It may well turn out that you’re right.
I believe the double well model—although it sounds somewhat specific at a glance—is actually a fully universal conceptual category over all relevant computational options for representing a bit.
You can represent a bit with dominoes, in which case the two bistable states are up/down, you can represent it with few electron quantum dots in one of two orbital configs, or larger scale wire charge changes, or perhaps fluid pressure waves, or ..
The exact form doesn’t matter, as a bit always requires a binary classification between two partitions of device microstates, which leads to success probability being some exponential function of switching energy over noise energy. It’s equivalent to a binary classification task for maxwell’s demon.
Summary of the conclusions is that energy on the order of kT should work fine for erasing a bit with high reliability, and the ~50kT claimed by Jacob is not a fully universal limit.
If you read landauers paper carefully he analyzes 3 sources of noise and kTlog2 is something like the speed of light for bit energy , only achieved at useless 50% error rate and or glacial speeds.
That’s only for the double well model, though, and only for erasing by lifting up one of the wells. I didn’t see a similar theorem proven for a general system. So the crucial question is whether it’s still true in general. I’ll get back to you eventually on that, I’m still working through the math. It may well turn out that you’re right.
I believe the double well model—although it sounds somewhat specific at a glance—is actually a fully universal conceptual category over all relevant computational options for representing a bit.
You can represent a bit with dominoes, in which case the two bistable states are up/down, you can represent it with few electron quantum dots in one of two orbital configs, or larger scale wire charge changes, or perhaps fluid pressure waves, or ..
The exact form doesn’t matter, as a bit always requires a binary classification between two partitions of device microstates, which leads to success probability being some exponential function of switching energy over noise energy. It’s equivalent to a binary classification task for maxwell’s demon.
Let me know how much time you need to check the math. I’d like to give the option to make an entry for the prize.
Finished, the post is here: https://www.lesswrong.com/posts/PyChB935jjtmL5fbo/time-and-energy-costs-to-erase-a-bit
Summary of the conclusions is that energy on the order of kT should work fine for erasing a bit with high reliability, and the ~50kT claimed by Jacob is not a fully universal limit.
Sorry for the slow response, I’d guess 75% chance that I’m done by May 8th. Up to you whether you want to leave the contest open for that long.
Okay, I’ve finished checking my math and it seems I was right. See post here for details: https://www.lesswrong.com/posts/PyChB935jjtmL5fbo/time-and-energy-costs-to-erase-a-bit