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There is a somewhat widely accepted argument that the second law of thermodynamics exists because the universe began in a low-entropy state. I'm writing a paper that mentions this (and must be finished today), but I've realised that I don't know who originated this idea. So does anyone know the original reference for this?


My paper is now submitted, but I'm still curious about the origins of this idea. @Sundak below gives the hint that Boltzmann might have been its originator. Based on this and a bit of searching, I was able to turn up his Lectures on Gas Theory, §90, in which he says "That in nature the transition from a probable to an improbable state does not take place as often as the converse, can be assumed by assuming a very improbable intial state of the entire universe surrounding us...", which sounds very much like the low-entropy big bang idea. However, what he's actually suggesting is that our local region of the Universe had fluctuated into a low-entropy state at some point in the past. He proposes this because he believes the Universe to be infinite in both time and space, implying that the universe as a whole must be in thermal equilibrium. He then goes on to say that at "distances $10^{10^{10}}$ times the distance of Sirius" there might be other civilisations for whom the arrow of time points in the opposite direction. Boltzmann is a fun guy to read. But the idea he's proposing here is not the same as the modern notion that the Universe simply started out in a low entropy state.

Skipping forward many decades, in the abstract for his 1979 paper Singularities and Time's Arrow, Roger Penrose describes the attribution of the second law to the universe's boundary conditions as being part of "the normal point of view". I suspect that the references in Penrose's paper might be a good place to look, but it seems that only the abstract is available online.

So that narrows it down to some time between 1896 and 1979, but probably towards the beginning of that period. It could well be that Boltzmann himself proposed the idea in a different work. If anyone has any further insight it'd be much appreciated.

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Not every idea has a published source, some are too simple. The idea of a low-entropy initial state is one of the too simple ones, like the idea of a dynamical vacuum after 1925, or the idea of quarks being like leptons in coming in left-handed doublets and right handed singlets in the standard model. These ideas were just understood collectively. – Ron Maimon Jul 15 '12 at 4:05

That was one of the options mentioned by Boltzmann, but he also entertained other options like Boltzmann brains.

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Do you have a reference to a specific work by Boltzmann where he mentions it? If you do it'd be really, really handy! – Nathaniel Jul 14 '12 at 10:46
I think I've found it: "That in nature the transition from a probable to an improbable state does not take place as often as the converse, can be assumed by assuming a very improbable state of the entire universe surrounding us..." taken from: 1896, Vorlesungen über Gastheorie: Vol I, Leipzig, J.A. Barth; translated together with Volume II, by S.G. Brush, Lectures on Gas Theory, Berkeley: University of California Press, 1964. – Nathaniel Jul 14 '12 at 10:53
I'll accept this answer tomorrow unless an even better one comes along. It's funny - for some reason I thought the main reference for this would be someone like Hawking or Penrose. Boltzmann continues to surprise me. – Nathaniel Jul 14 '12 at 10:54
Ah, it looks like I misunderstood the above quote. He's not saying we should assume an improbable initial state, just an improbable state at the present time. But this doesn't work as an argument because it would lead us to expect high entropy in the past as well as the future. :( – Nathaniel Jul 14 '12 at 17:18
D'oh! He does say "initial state", I just mis-typed it in my earlier comment. However, he's actually just referring to our local part of the universe, which he suggests could have fluctuated into a low entropy state. This means I'm still looking for the original reference for the idea that the universe began in a low entropy state. (It might well be a different work by Boltzmann.) – Nathaniel Jul 14 '12 at 17:37

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