I am having a difficulty understanding why second law of thermodynamics is still a valid universally accepted concept. I understand it works on paper for describing isolated heat systems. However, I do not understand how can it hold place as a valid concept on our path towards a theory of everything. I would like to generate a discussion around some ideas I have that brought me to this conclusion. Maybe there is someone out there who's also thinking about this. Maybe you've got time to point out errors in my logic or suggest reading.

Physicists assume matter and energy is conserved and also tell us "entropy increases!". According to information theory, entropy is related to information. The relationship is "when entropy increases information decreases". (Very short summary)

Now if entropy increases then at some point in the past there was less entropy. So if you go all the way back to Big Bang entropy was at minimum and the amount of information was at maximum. Well, there seems to be something contradictory here! In the present day picture, information is more abundant than ever, we have galaxies, particles, planets, life and all the other stuff, and at Big Bang or slightly after we just had some radiation.

From this, I can't understand why people state that entropy is increasing. Any useful insight?

  1. That the early universe was in a very low entropy state is, in fact, one of the most confusing open questions in physics. As of now, it is really nothing but an initial condition put into the equations, but it seems strange, a priori, that time should start in such a state. As of now, there are no definitive answers for why the early universe was low-entropy, aside from heuristics arguing that we know the direction of time only from the change in entropy, so if you have some sort of fluctuation model of entropy, time seems to be going 'forward' on either side of an entropy minimum, even if these directions of time are opposite in some absolute sense. That the low entropy state coincides with the big bang would be an interesting result if it was predicted by some new theory of physics that solved the GR/QFT problem.
  2. Saying that entropy is 'information' can be useful in some senses, and can be confusing in other senses. When you are talking about primordial gas existing before humans did, it is probably best to think of entropy as measuring 'order' more than it is measuring 'information'--the early universe appeared to be in a VERY ordered state, where the gas had nearly constant density temperature and pressure--if you are DESPERATE to think of this in terms of information,w hat this means is that, in this state, knowing the properties in the gas at any point is almost completely possible from knowing the properties of the gas at any other point, no matter how far away--one bit of information gives you access to all of the rest of the information.
  • $\begingroup$ I think I see your point - mathematically a uniform gas is a more ordered thing than a planet or a galaxy... by this logic however nothingness is the next most ordered thing which is kind of paradoxical... $\endgroup$ – nebulus Nov 6 '12 at 21:08
  • $\begingroup$ to bad ln(0) does not exist $\endgroup$ – nebulus Nov 6 '12 at 21:18
  • $\begingroup$ Another point is... air is most uniform when entropy is high... there is also a contradiction here as well... unless the gas was somehow uniform in a different way... $\endgroup$ – nebulus Nov 6 '12 at 21:47
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    $\begingroup$ @seaworthy: there's only so far that a qualitative description will take you. The formal definition of entropy is $S = k \ln \Omega$, where $\Omega$ is the number of indistinguishble descriptions a state will have. If every particle is in an identical state, you only have one description, and $S=0$. If every particle but one is in its ground state, then you have $S = k \ln N$. At higher energies you have to do combinatorics and the factors grow very quickly. $\endgroup$ – Jerry Schirmer Nov 7 '12 at 6:54

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