**Entropy puzzles:**

- If you find yourself in a universe with low entropy it is as likely to have come from a higher entropy state as it is to evolve into a higher entropy state. So how do you know you are not a Boltzmann brain?
- Take a box with a partition in it, with gas A on one side, gas B on the other side, and both gases are at the same temperature and pressure. Remove the partition. If gas A and B are different gases, there is an entropy that arises due to the mixing. If the gases are the same, no additional entropy is calculated. What if you thought they were the same gas and years later it was discovered that they happened to be two different isotopes? (See Gibbs paradox and E.T. Jaynes' paper). More generally this microstate / macrostate business seems completely user defined and arbitrary, so how can it have real physical effects?
- In a reversible system there must be just as many paths that decrease the entropy as that increase the entropy. Why don't we observe as many of the first type as the second?
- A gas squeezed in the corner of a room will tend to spread thereby increase its disorder and entropy. If we add an attractive force like gravity matter seems to clump together rather than spread out. How does clumping together increase entropy?
- A rotting plant turns into dust and gas which increases disorder and entropy. A seed turns a bunch of gas and dust into a full grown tree which seems to decrease entropy. This can only happen because the seed is not a closed system and is using the energy from the sun and ends up increasing the overall entropy of the universe at the end. When, how, and why does this type of thing happen?

**Further reading:**

- From Eternity to Here: Sean Carroll's book that inspired this post.
- Labyrinth of Time: Michael Lockwood's book on the arrow of time with a bit more philosophy and a bit less black hole physics.
- Time and Chance: David Z. Albert's book gives one of the clearest discussions of thermodynamics (both classical and statistical) and its relation to the arrow of time.
- Good and Real: Gary L. Drescher's book that tackles not only the arrow of time, but quantum indeterminacy, consciousness, free will, and ethics. This is one of my favorite books which inspired a few earlier posts.
- E. T. Jaynes has a number of articles that clarify some of the mysteries. See also these links.
- Permutation City: One of my favorite sci-fi novels by Greg Egan explores the nature of time, simulation and reality. Maybe instants are not ordered in time at all, the state of our short term memory seems to give this impression.
- Max Tegmark at MIT came up with the Mathematical universe hypothesis which is reminiscent of the Dust theory that underlies Permutation City. See also Hans Moravec's essay.

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