Chalnoth said:
While there is some relationship between chaos/disorder and entropy, the problem is that the former terms are colloquial terms that are very non-specific, and may lead people to incorrect conclusions.
For example, consider a room with air in it, with the air in two different configurations. In each configuration, the air has the exact same amount of total energy, and there are the exact same number of molecules. The difference is on where the molecules are:
1. In the first configuration, the air molecules are spread out almost evenly. If you pick any two cubic centimeters of air in the room, the number of molecules in each cubic centimeter is likely to vary by less than one in a billion.
2. In the other configuration, the air molecules are gathered in clumps, so that one cubic centimeter of air might have a million times as many molecules than another.
Which of the two configuration seems to be more chaotic and disordered? Presumably you would answer configuration 2. But it is configuration 1 that has the higher entropy (much higher, as it turns out, as evidenced by the fact that we never run into a room like number 2).
As for the universe as a whole, the eventual, maximal-entropy configuration appears to be empty space.
Entropy in cosmology is also confusing, in your example you are describing closed systems, which is the more classical form of entropy. In open cosmology systems its more tricky and in a sense what defines order or disorder.
http://philsci-archive.pitt.edu/4744/1/gravent_archive.pdf
the above article discusses some of the misconceptions of what ppl might think of as low entropy or high entropy in cosmology usage.
Its claim:
the assumption that uniformity equates to high entropy ignores the existence
of gravitation. Given the attractive nature of gravity (it is claimed), a uniform
state is actually much lower-entropy than a much more clumped state. Various
forms of argument are given for this; frequently, it is argued that when attractive
long-range forces are present, matter has a higher entropy when highly concentrated
than when diffuse.
[T]he attractive nature of the gravitational interaction is such that
gravitating matter tends to clump, clumped states having larger
entropy. . . . For an ordinary gas, increasing entropy tends to make
the distribution more uniform. For a system of gravitating bodies the
reverse is true. High entropy is achieved by gravitational clumping
there are numerous examples of some of the confusions with regards to entropy usages in cosmology.
I would would be curious on how some of the views of this paper have been resolved into more current cosmology entropy usage and definition. For example entropy in the second law of thermodynamics is a closed system. So how is it used in cosmology which could be an open or closed system globally ?