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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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Mozibur Ullah
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    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. – CuriousOne Dec 29 '14 at 17:38
  • 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. – John Rennie Dec 29 '14 at 17:45
  • @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. – Mozibur Ullah Dec 29 '14 at 17:53
  • 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. – Mozibur Ullah Dec 29 '14 at 17:55
  • Its worth pointing out too, I think, that Feynman wasn't aware of the atomic hypothesis in Antiquity, and nor the role that it played in the formulation of Modern physics; I forget how far he traced it back, but it would be sometime in the modern classical era. – Mozibur Ullah Dec 29 '14 at 18:08
  • Calculations in physics are done for the sole purpose of finding testable hypotheses. Calculating a theoretical quantity that can not be measured is, strictly speaking, an empty scientific exercise. The latter doesn't apply to atomism, at all. It can be verified (or it could have been falsified to this day) experimentally just fine. But like I said, the greater conceptual difficulty here stems from the assumption of known system boundaries. – CuriousOne Dec 29 '14 at 18:51
  • @curiousOne: I can't say I fully agree with this; after all the entropy of a black hole cannot be directly measured - but its calculated all the same; what cannot be done is calculating a figure for a quantity that is, in principle indeterminate. – Mozibur Ullah Dec 29 '14 at 19:01
  • So how do you know that the calculated black hole entropy is correct? Unless you start a church of Hawking-Bekenstein and make it a matter of faith, it's not validated physics until we have a way of measuring it. – CuriousOne Dec 29 '14 at 19:05
  • @curiousOne: I don't; but haven't you heard of the role of hypothesis in physics? The 'string' hypothesis, the 'causal net' hypothesis and so on. Hypotheses may take a long time to verify, and even then they maybe verified only in part; also, I'd argue that in part, the theory of knowledge in physics isn't purely empirical, it is to a large degree, but it is also coherent with verified physics; but the whole picture is complex. – Mozibur Ullah Dec 29 '14 at 19:12
  • "The entropy of a perfect crystal, at absolute zero (zero kelvins), is exactly equal to zero." (Third law of thermodynamics) Does this answer your question? – Wood Dec 29 '14 at 20:06
  • The role of hypotheses in physics is to be tested experimentally. Unless they can be tested, they are worth about as much as the paper they have been published on. – CuriousOne Dec 29 '14 at 20:29
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    @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. – Mozibur Ullah Dec 30 '14 at 10:32
  • @Wood: possibly. – Mozibur Ullah Dec 30 '14 at 10:33
  • How are you going to measure the entropy of the entire universe IN THE PAST? I am waiting for constructive experimental suggestion. :-) – CuriousOne Dec 30 '14 at 14:43
  • @CuriousOne: well, I'm not an experimentalist; but one does gather that certain relics dating from times close to the Big Bang have been identified - Cosmic Background Radiation; the study of that might give some evidence towards that. But you haven't answered the question I was asking...too difficult for an unsubtle epistemology of science? – Mozibur Ullah Dec 31 '14 at 15:03
  • Nope. These are models that can tell you something about things local to the INSIDE of the universe. They are utterly useless to make predictions about its OUTSIDE. It's not even a question of difficulty. Science can't answer thermodynamics questions about an experimentally ill-defined system. – CuriousOne Dec 31 '14 at 15:13
  • @curiousone: What of it? you're simply alluding to object/subject divide; QM still works, even though that question is and remains a source of philosophical-physical debate; Science (as much else) proceeds by idealisations, and models and concepts do change; is it worth reminding you that Newtonian Gravity, for example 'worked' even if, as Newton admitted, action at a distance is ill-defined. Still avoiding MY question...? – Mozibur Ullah Dec 31 '14 at 15:25
  • I am simply alluding to the definitions employed in thermodynamics. Physics is all about reading the fine print. If the fine print does not apply the theory does not apply and no level of glossing over this can change that. Your question was ill-defined in the beginning at it is still ill-defined. From a scientific perspective "action-at-a-distance" is not science. It's a philosophical term that is undecidable by observation. Newton didn't like it... but then he didn't like relative space, either, even though he proved the relativity of mechanics in his own book. – CuriousOne Dec 31 '14 at 16:52
  • @curiousone: physics isn't just about reading fine-print; though I agree that counts; action at a distance is not just a philosophical problem; if you think about it carefully you'll notice that this physical anomaly was solved by Einstein - force transmitted by the curvature of space; if you dispute entropy is ill-defined for the universe at or at times close to the Big Bang; is it worth considering the entropy of the universe now - or is that ill-defined too? – Mozibur Ullah Jan 02 '15 at 13:56
  • And if it isn't; then what about yesterday, or a billion years ago, or 13 Billion? – Mozibur Ullah Jan 02 '15 at 13:57
  • Is there some law of continuity that connects them? or not? – Mozibur Ullah Jan 02 '15 at 13:57
  • Einstein told you what gravity is and why it acts at a distance? No, actually, he didn't. He told you how to calculate it better than Newton did. Force is transmitted by the curvature of space???? There is no force. Never has been. And space doesn't have curvature. Spacetime has curvature. Told you the fine print matters. I am also telling you that you won't like real physics... you just don't know what real physics is. Have a nice day. – CuriousOne Jan 02 '15 at 16:03
  • @curiousOne: This is a letter from Newton to Bentley "That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it". – Mozibur Ullah Jan 03 '15 at 13:49
  • Although I have no evidence to the contrary, I think its reasonable to suppose that Einstein didn't fall into that particular trap (after all he called Quantum Entanglement spooky action at a distance); I didn't, but did you whilst doing all those calculations...which tells us what gravity actually is? – Mozibur Ullah Jan 03 '15 at 13:52
  • Yep, that's a very well known letter of Newton, which tells us what he thought, and nothing else. That's nice for the history of science department and... for nothing else. Einstein, of course, was wrong about entanglement. There is no action in it, at all (please read up on the definition of action in physics). He then proceeded to spend the rest of his life on classical field theory, which does not describe nature correctly. That is tragic and... nothing else. – CuriousOne Jan 03 '15 at 14:48
  • @curiousOne: I find it suprising that you're putting yourself ahead of physicists of the stature like Newton & Einstein; and also suprising that you can't, or find it difficult to distinguish the conventional notion of action from that of Einstein-Hibert Action; an action, that I'm sure you'll be careful enough to note named after Einstein and (not after you); – Mozibur Ullah Jan 03 '15 at 18:54
  • My God, to call a mans life tragic, when he was friends with mathematicians of the stature of Godel & Hilbert, established the atomic hypothesis via a mathematical treatment of Brownian motion, established Relativity - both the Special & General theory, established too the quantum explanation of photo-electric effect (for which he won the nobel prize for)...what exactly counts as an achievement in your mind? – Mozibur Ullah Jan 03 '15 at 18:55
  • Einstein-Hilbert action has nothing to do with entanglement. I can sense, though, that you are very needy for attention... and I really don't care. Have a good one. :-) – CuriousOne Jan 03 '15 at 18:57
  • You're a troll, aren't you? And an arrogant one at that too. Somehow you've learnt the language of physics without actually understanding any of the physics; I didn't realise that they came wearing physics hats...try changing your name to CuriousZeroArrogantTroll; as thats a more truthful representation than your current handle... – Mozibur Ullah Jan 03 '15 at 19:03
  • You may be interested in this paper, in which jaynes in part argues that entropy has a fundamentally anthropomorphic character: http://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf – s.harp Aug 17 '15 at 16:06

3 Answers3

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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.

pwf
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  • +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. – Roger V. Aug 20 '21 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!

Carcassi
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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.

Guill
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    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? – Mithoron Feb 13 '15 at 20:23