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My understanding is that to define the entropy of a system what you have to do is as follows:

  1. Define the boundaries of your system.
  2. Define a set of "microstates" of the system.
  3. Define a partition of microstates of the system where each element of the partition is measurable and known as a "macrostate".

The entropy of the system in some macrostate A is the logarithm of the measure of the microstates contained in mactrostate A.

Now, I often hear cosmologists say things like "the entropy of the early universe was low." What I understand that to mean is that for some specific partition of the microstates of the universe P, the state of the early universe was contained in some "small" element of that partition.

What I am trying to know is: What is this partition P which is being implicitly referred to? (And optionally, what is special about that partition which allows us to not be explicit about it?)

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    $\begingroup$ Well what macrostates do you usually see defined for systems? Is there any reason you think they cannot be applied to systems as large as the universe? (I am not saying whether or not I think it would be valid, I just think it would be helpful to know what you know and have thought through so far). $\endgroup$ Commented Apr 1, 2019 at 14:36
  • $\begingroup$ Usually, either amount of energy, or distribution of energy or distribution of mass or distributions of different kinds of matter. I think all can apply, but they don't say the same thing about a system. For instance, I could have really high entropy wrt spacial distribution of mass and really low entropy wrt distribution of energy among ptcls in my system. (Say, a single ptcl has all the energy and all the others are spread uniformly throughout space) $\endgroup$
    – azani
    Commented Apr 1, 2019 at 14:50
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    $\begingroup$ Ok. And why do you think these do not apply to the universe? You always have to specify the macrostates you are looking at regardless of the scale of the system in question. Right? $\endgroup$ Commented Apr 1, 2019 at 15:11
  • $\begingroup$ Right. But I often hear cosmologists say things like "the early universe had low entropy" without stating what the macrostates are. So, what macrostates are they talking about? $\endgroup$
    – azani
    Commented Apr 1, 2019 at 16:14
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    $\begingroup$ @GarethMeredith That's not what the third law of thermodynamics says. The third law of thermodynamics says that a perfect crystal at absolute zero has zero entropy. $\endgroup$ Commented Apr 1, 2019 at 19:02

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