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Following this question on the Entropy at the Big Bang where I asked:

Since Entropy always increases (in general); its expected that the entropy at the beginning of the universe should be the lowest possible.

One answer to this by Chris White suggested that:

This is a logical fallacy. From the premiss "entropy always increases," we can derive the conclusion "the entropy at the beginning of the universe was lower than it is now." We cannot from this one premiss say anything about the absolute entropy back then. In particular, there is no reason it need be close to zero or a minimal value in any sense. Is simply cannot be maximal.

But this seems to be, to some extent invalidated by another answer where its stated that

The quark-gluon plasma has been shown to be a [minimal entropy fluid] .

This plasma existed a few milli-seconds after the Big-Bang; it seems rather incredible that entropy can be at a minimum slightly after the Big Bang, but not at it (if or when this can be given a meaning).

This leads to a question: If the Quark-Gluon plasma is as far theoretically we can go far back, and its entropy is at a minimum; then can we not set it as zero - thus making entropy absolute, in the same way that temperture is absolute.

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    $\begingroup$ Anybody who suggest that they can calculate the entropy of the early universe needs to take a step back and read the empirical definition of science, again. The greater conceptual difficulty with "the entropy of the universe" is the observationally so far undecidable question if the currently visible (or theorized) universe is actually the whole universe. As a result the question of total entropy is fraught with danger of making invalid thermodynamic assumptions. $\endgroup$
    – CuriousOne
    Dec 29, 2014 at 17:38
  • $\begingroup$ Agreed. The issue of the entropy of the early universe is one that has no clear resolution. Mainstream physicists (Roger Penrose springs to mind) differ vehemently on the subject. $\endgroup$ Dec 29, 2014 at 17:45
  • $\begingroup$ @CuriousOne: firstly there's a world of difference between calculating the entropy at the Big Bang, and suggesting that it has a determinate value, and that determined value is at a minimum; secondly, you're under-emphasising the role of hypothesis (and thus speculation) in your defence of empirical science. After all, the most marvellous suggestion of Atomism, and as pointed by a figure no less than Feynman as the most important hypothesis in all of physics wasn't first formulated in classical physics (ie since Galileo), but in Antiquity. $\endgroup$ Dec 29, 2014 at 17:53
  • $\begingroup$ When there was no actual hope of testing the hypothesis, and one can pursue this hypothesis through Lucretious, Daltons Atoms, Newtons Corpuscules and modern quanta. It took, in actual fact, over 2500 years before this suggestion could be verified experimentally. $\endgroup$ Dec 29, 2014 at 17:55
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    $\begingroup$ @curiousOne: Please tell me how this actually applies to the atomic hypothesis which was formulated 2500 by Democritus, Leucippus and Epicurus; lionised by Lucretious in De Rerum Natura and which was circulated in renaissance Italy, so at the beginning of the classical modern era, and also in Newtons library where he made assiduous notes and inspired his corpuscular theory. How does your characterisation of 'hypothesis' explain this. It seems to some extent wanting, at least historically, and thus also in a contemporary context, if we are to take the lessons of history seriously. $\endgroup$ Dec 30, 2014 at 10:32

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In classical thermodynamics, only changes in entropy ever matter ($dS = \dfrac{dQ}{T}$ for reversible processes), so it is not meaningful (though it may be convenient) to define an absolute entropy.

HOWEVER, in statistical mechanics, entropy has a probabilistic interpretation: $S = -k_B\sum_i p_i ln p_i$, where $k_B$ is Boltzmann's constant and $p_i$ is the probability that a system in a given macrostate will be in the $i$th corresponding microstate. If the probabilities are determined, then this constitutes an absolute measure of entropy.

HOWEVER, applying this absolute measure to the entire universe is problematic, because applying probabilities to the universe as a whole, with no evident parent distribution to be sampling from, is not well defined.

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  • $\begingroup$ +1 since the answer actually points out that there are different ways to define entropy, including the axiomatic definition (the quantity that always increases). Jaynes claims that thete are at least 6 ways to define entropy - the Shannon's formula in the answer is information entropy, which is not always the same as meant in statistical physics. $\endgroup$
    – Roger V.
    Aug 20, 2021 at 19:02
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Yes, thermodynamic entropy is absolute. No need to invoke early universe, just the Third Law of Thermodynamics. If the system has only one possible configuration (i.e. a perfect crystal at zero temperature), the entropy is zero. Not the lowest: zero.

Another way to look at this: if you try and rescale, the entropy would cease to be extensive. Suppose you have $S_A + S_B = S_{A+B}$, where $A$ and $B$ are two independent systems and $A+B$ the composite. If you rescale by a constant $c$ all quantities, you have $S'_A + S'_B =(S_A + c) + (S_B + c) = S_{A+B} + 2c = S'_{A+B} + c$. So $c$ has to be zero to make the new entropy extensive again.

Personally, I like to think of zero entropy as the entropy of an empty system. You can't go lower than that. Hope it helps!

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Strictly from a logical point of view, If the universe's entropy,is always increasing, it follows, that the universe's entropy must have been at a minimum (but not zero), "shortly after" the Big Bang.

Just like we don't know if there is something "colder" than -273 degrees Celsius, because we can not measure it, we can not find the entropy of the universe at the BB. However, I agree that just like we defined absolute zero temperature as -273 (0 Kelvin), we could define the universe's entropy, "shortly after" the BB, as a minimum (but not zero). Hopefully, this would serve a useful purpose.

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    $\begingroup$ We don't know if universe's entropy is always increasing, and are you even talking seriously about defining arbitrarily the entropy of the universe? $\endgroup$
    – Mithoron
    Feb 13, 2015 at 20:23

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