# Is entropy absolute (as in absolute temperature)?

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.

• 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
• @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

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.