Let's start with the classic Maxwell's Demon setup.

We have a container of gas, i.e. a bunch of molecules bouncing around. Down the middle of the container is a wall with a tiny door in it, which can be opened or closed by a little demon who likes to mess with thermodynamics researchers. Maxwell[1] imagined that the little demon could, in principle, open the door whenever a molecule flew toward it from the left, and close the door whenever a molecule flew toward it from the right, so that eventually all the molecules would be gathered on the right side. That would compress the gas, and someone could then extract energy by allowing the gas to re-expand into its original state. Energy would be conserved by this whole process, since the gas would end up cooler in proportion to the energy extracted, but it would violate the Second Law [...]

The original text contained 2 footnotes which were omitted from this narration.

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First published:
August 26th, 2025

Source:
https://www.lesswrong.com/posts/DHSY697pRWYto6LsF/do-divergence-a-bound-for-maxwell-s-demon

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Narrated by TYPE III AUDIO.

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Images from the article:

Illustration showing dots moving from left side to right side

Diagram showing three points A, X and O with connecting arrows and π symbol.

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“Do-Divergence: A Bound for Maxwell’s Demon” by johnswentworth, David Lorell

LessWrong (30+ Karma)

“Do-Divergence: A Bound for Maxwell’s Demon” by johnswentworth, David Lorell