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Comment by tedsanders | Hacker News Reader

It's a common misconception that the Landauer Limit, which says it takes kT*ln(2) energy to erase a bit, "solves" Maxwell's demon. That argument is actually circular, because the Landauer Limit relies on the Second Law in its derivation. I cannot find the source now, so it's possible I'm wrong, but my recollection is that even Bennett, who advanced the argument in 2003, eventually admitted as much around 2006/2007, if memory holds.[1]

I spent years of my PhD reading and thinking about these topics, and made some contributions to these Wikipedia pages years ago.

[1] https://en.wikipedia.org/wiki/Landauer%27s_principle#Challen...

(To be clear, I am not saying that Landauer Limit or the Second Law are wrong - just that it's wrong to use the Landauer Limit to "prove" the Second Law.)

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Isn't there no "proof" within the laws of physics for the second law? - you must posit a "Past Hypothesis".

Depends on what level. Historically it was an empirical observation that was taken in as an axiom to classical thermodynamics. So it couldn't be derived from other laws.

If we move to statistical mechanics we can derive the second law from probabilities. In essence it is possible for any system to break it, it's just very very improbable. Just like if you toss a coin billions of times. It's possible for you to get more, or less, than half of the tosses to be heads. It's just very very improbable to get anything more than very tiny deviations.

But when we apply statistical mechanics to "microscopic" arrangments like a few particles in an idealized rigid box or in a vacuum, there is no arrow of time. The laws of physics themsleves are totally symmetric (CPT theorem), and it is not thought the t-asymmetry of the weak interaction is responsible for the global macroscopic arrow of time. So without some statement of initial/prior conditions, we have no reason to see just the "forward" arrow unless we say something about initial/prior conditions. (Loschmidt's Paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox)

You can prove it in the context of Ergodic theory. Though that's a model so assuming that it correctly approximates the real world is still an assumption.

Are you sure Ergodic theory does the trick? When I hear people like David Albert or Sean Carroll speak, they always make clear you need some kind of initial/prior conditions or else stat mech does not guarantee why we only see the forward arrow of time. If we assume we can reduce all physical process to the behavior of fundamental particles (or fields), and the physical laws that describe the microscopic world are entirely symmetrical (CPT theorem), you get Loschmidt's Paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox. They say the Past Hypothesis (low entropy big bang prior condition) is necessary to resolve it.

*And the t-assymetry of the weak interaction isn't the reason according to the wikipedia article on time asymmetry - you still need initial conditions. "Time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe. "

Well it doesn't tell you why the original state of the universe had such a low entropy, but it can at least be used to show that entropy should increase from there.

Do you have any recommendation for a book? I studied classical thermodynamics (and physics) long ago and I consider I have good probability and statistics foundations but never studied statistical mechanics. From my ignorance I cannot understand how is it possible that entropy considerations (macroscopic) are applicable to a microscopic demon.

The idea is that temperature alway gives you an energy distribution p(E) =exp(-E/kT)*const. https://de.m.wikipedia.org/wiki/Boltzmann-Statistik if you want to store information with one particle in a double well potential (tiny ist information storage), you need the barrier at least so high that you don't just hop to the next bin due to these fluctuation. This means you have to introduce a minimum energy effort depending on temperature needed to delete the information later.

Ps statistical physics is slightly weird, not sure about a good book. Maybe Berkeley physics course vol 5 or so.

About the Landauer principle itself I remember the paper actually to be quite accessible.

I'm not aware of a good book, but here's a website that has finally made me understand postmodern thermodynamics : (Though I perhaps have a non-common path of learning modern thermodynamics, then skipping basic physical statistics, only to jump into advanced physical statistics later ?)

http://www.av8n.com/physics/thermo/entropy.html

Some core ideas :

- 19th century modern thermodynamics are hopelessly obsolete (at least if you want to understand the "why" and/or do stuff more advanced than "basic" heat engines ?) with tons of confused notions like "heat".

- The term "thermodynamics" itself is bad, "energo-informatics" would perhaps be a better one ?

- Entropy is just a redundant term for (the lack of) information about a system (= macrostate = distribution).

- Hence, you need at least some quantum mechanics : Heisenberg's unsharpness principle (and Plank's constant h) to be able to build the theory from the microstate up, because you need to be able to quantize position and momentum to define information.

- disorder is another of those misleading terms

I think of it as saying that the two are really just equivalent to one another, in a different basis. At a mathematical level, there's a fine line between "proof" and "redefining your terms".

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