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 initial 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.

  • $\begingroup$ That was one of the options mentioned by Boltzmann, but he also entertained other options like Boltzmann brains. $\endgroup$
    – user10574
    Jul 14, 2012 at 10:38
  • 1
    $\begingroup$ 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. $\endgroup$
    – Ron Maimon
    Jul 15, 2012 at 4:05
  • $\begingroup$ where is the paper you wrote (that gave rise to the question) published? $\endgroup$ Jun 17, 2016 at 13:38
  • $\begingroup$ @ArnoldNeumaier I'm pretty sure it was this one goo.gl/FE6mWv , published in the proceedings of a MaxEnt conference. Maybe one day I'll publish something of greater note on this stuff. $\endgroup$
    – N. Virgo
    Jun 17, 2016 at 13:48
  • $\begingroup$ @N.Virgo The URL shortener now points to some shady website. However, I was able to find a copy of your paper saved on the Wayback Machine $\endgroup$
    – user337588
    Jun 17, 2022 at 9:25

3 Answers 3


So that narrows it down to some time between 1896 and 1979

The second law was known to Clausius, and trivially implies the knowledge that the entropy in the far past was much less than now. (That is, if one is permitted to apply the notion to the universe as a whole; cf. below.)

It seems that Clausius stated explicitly (in 1856) only the extrapolation to the far future, not the far past:

The entropy of the universe tends to a maximum.

This is based on a very informal, hence not really conclusive argument. Exactly the same argument ''proves'' that the entropy of the universe began in a minimum.

On the other hand, the term 'big bang' was coined only in 1949, and the microwave background radiation that gave credibility to the big bang was discovered only in 1965. Thus the uncertainty interval can be narrowed to 1965-1979.

In his book ''The character of the physical law'', Cambridge, Mass. 1965, Feynman says on p.116:

I think it necessary to add to the physical laws the hypothesis that in the past the universe was more ordered, in the technical sense, than it is today - I think this is the additional statement that is needed to make sense, and to make an understanding of the irreversibility.

He doesn't apply it to the beginning of the universe, though.

Since the Big Bang is a singularity, the notion of entropy at the big bang makes anyway no sense. It is not even clear what the entropy of the whole universe should mean and whether it can be defined at any time. (It is likely to be infinite always, according to any sensible definition.)

Thus it is not really clear what you are asking for.

  • $\begingroup$ I tend to think that with the statistical definition of entropy, which counts the available microstates for a given macrostate, at the approach to the singularity the number of microstates diminishes , due to the reduction of phase space. At the classical singularity there is only one microstate by construction. How wrong is this reasoning ? $\endgroup$
    – anna v
    Jun 11, 2016 at 11:11
  • $\begingroup$ I know very well that the concept doesn't quite make sense, but that isn't the point of the question. The point of the question is to identify the place where it was first proposed, precisely in order to be able to convincingly argue against it. It is evident that this was a long time after Clausius, as explained in the question. $\endgroup$
    – N. Virgo
    Jun 11, 2016 at 12:13

As you and others have said, it looks like Boltzmann could plausibly be credited with the idea that the universe had a low-entropy past:

The second law will be explained mechanically by means of assumption A (which is of course unprovable) that the universe, considered as a mechanical system—or at least a very large part of it which surrounds us—started from a very improbable state, and is still in an improbable state.

(As excerpted in From Eternity to Here (1) ).

However, the actual identification of the Big Bang with this low-entropy boundary clearly took place later. It is possible that this idea was so natural that no one made a big deal of saying it explicitly, but this might also represent a hindsight bias.

Here's one interesting intermediate step: it appears that the first applications of cosmology to the arrow of time problem came mostly by supporters of steady-state cosmology, who were influenced by the Wheeler-Feynman absorber theory of electromagnetism. J. Hogarth did a PhD thesis in 1953 which connected cosmological expansion with the breaking of absorber-emitter symmetry (2, 3), and T. Gold proposed in 1962 that entropy increase (and thus the entropic arrow of time) follows the direction in time in which the universe is increasing (4). I can't find any indication of who first applied this to Big Bang cosmology specifically. But by the time that the CMB results came in it appears that this idea was well-known by the steady state community, so perhaps as that theory lost support it became a natural direction to go in. Penrose himself may have figured in this part: he attended a conference on cosmology and the arrow of time in 1963, along with Feynman (who famously insisted that he be called Mr. X in the proceedings), Wheeler, and many steady state people. But I can't find any relevant writings by him from that period.


Here are some references:

Time and chance by david Albert

Time's arrow by huw price

From eternity to here by sean carroll

The direction of time by H. D. Zeh

Physical basis of time Asymmetry by paul davies

There are many other excellent books or articles about the subject. Especially, in relation to the foundation of statistical mechanics I saw Two good books:

The Road to Maxwell’s Demon By MEIR HEMMO and ORLY R. SHENKER

Physics and chance by lawrence sklar.

To statrt I highly recommend to read an article (difference between Past and future) by Feynman (in the book The character of the physical law) who was one of the first physicists that stress on the low entropy Quality of the far past or big bang to jastify the observed arrows of time in the cosmos.


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