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Say we have a planet and we blow it up to tiny pieces that gets spread out in a cloud of debris around the planets original location. This cloud of debris is analogue to a cloud of water wapor in terms of entropy: many many underlying arrangements of atoms can give rise to the macroscopic phenomenon of a debris cloud/wapor cloud.

Now let time pass. Let's say that no rotational movement was introduced in the debris cloud. In time, the debris cloud will collapse upon itself, perhaps rebounce a bit, but finally settle into a new planet much like the old planet. In this new state, the entropy is lower than in the debris cloud state. Fewer underlying constellations give rise to the macroscopic roundness of a planet. In order to make the debris cloud into a planet, energy had to be used. Gravity accelerated the debris until the round shape was achieved. Heat was generated as a byproduct.

Normally, when time passes, entropy is increased. But in this case, the local entropy of the debris cloud was decreased. Am I right that this case is unusual?

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    $\begingroup$ ...no more unusual than a cloud of water vapor evaporating from the ground, and coming back down as rain. $\endgroup$ Commented Aug 2, 2015 at 0:46
  • $\begingroup$ But this is also a consequence of gravity. My point is that forces has the special ability to create low entropy (locally). Much like an air conditioner can. Can we come up with any example of the creation of low entropy (locally), in an imaginary world where no forces exist? $\endgroup$
    – loldrup
    Commented Aug 2, 2015 at 2:09

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The entropy increases always. There is nothing unusual about the example of planet formation. Either one of two things has to happen when the dust contracts into a planet:

  • The planet heats up as the dust contracts, increasing entropy.
  • Heat is radiated into empty space, decreasing the entropy of the collection of dust but increasing the entropy of the rest of the universe.

You know the particles must heat up, since they are "falling" together to form a planet, thus gaining energy.

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  • $\begingroup$ I know, but I was talking about the 'unusualness' of creating local entropy reductions. $\endgroup$
    – loldrup
    Commented Aug 2, 2015 at 7:37
  • $\begingroup$ @loldrup But local entropy reductions happen all the time. Every single living organism is a local entropy-reducer. Every time heart flows from a hot object to a cold object, entropy is reduced in the hot object. $\endgroup$ Commented Aug 2, 2015 at 13:42
  • $\begingroup$ And my point is that the entropy of the planet is NOT necessarily reduced. It is reduced if it emits enough thermal energy; however, if we put it in an isolated box, the planet would just heat up, and its entropy would NOT decrease. $\endgroup$ Commented Aug 2, 2015 at 13:43
  • $\begingroup$ If we put the planet in an isolated box then indeed it would heat up. However it would still end up being round. I see roundness as a more ordered pattern than 'cloud of debris'. So, I guess one factor contributed to entropy reduction (the generated roundness if the planet) and another factor contributed to entropy increase (the increased velocity of all the atoms). Does this sound reasonable? $\endgroup$
    – loldrup
    Commented Aug 2, 2015 at 14:05
  • $\begingroup$ Also, I like your comparison with living organisms. Living organisms have to work hard with complex machinery in order to create local reduction of entropy. Gravity can manage this simply by being a force of nature! Pretty neat I'd say! $\endgroup$
    – loldrup
    Commented Aug 2, 2015 at 14:05
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In time, the debris cloud will collapse upon itself, perhaps rebounce a bit, but finally settle into a new planet much like the old planet. In this new state, the entropy is lower than in the debris cloud state.

This is false. You are associating a subjective appreciation of disorder to entropy, and entropy is not disorder. Even if the cloud seems "disordered", its state is less probable than the last contracted state.

The expanded cloud has lower entropy than the contracted state. You will ask yourself how did entropy decreased when the planet exploded, and it is you that should answer: why did it exploded? Probably some kind of explosive energy was concentrated on the planet (energy useful to do work). I will assume a huge atomic bomb. So, entropy grows as this:

  1. There is an atomic bomb in the planet (replace it with whatever explosive source you like). The planet is a concentrated sphere of matter+bomb. Entropy is the lowest.
  2. The bomb explodes, bomb energy disperses, matter disperses but acquires potential energy. Entropy has grown, but it is still low.
  3. Gravity forms a planet. Energy dispersal is maximal. Matter has no potential energy, bomb does not exists anymore. Entropy is at its maximum.

I assume you will think that with time, matter can get organized until becoming a bomb again, which will eventually explode again and repeat the cycle. In this case, entropy never grows. The system behaves like a pendulum and the fact that the planet becomes a cloud of rocks does not mean that entropy has increased. Entropy is not disorder. See my answer to pendulum entropy here https://physics.stackexchange.com/a/408846/133118

Entropy is not related with the position of the rocks, but to energy. If energy disperses, entropy grows. But the fact that a pendulum is on the lowest position (all potential energy has dispersed) does not mean that entropy has grown. At such instant, kinetic energy is at its maximum. Entropy is not related to a single type of energy manifestation on the system, but to all types of energy: remember that it corresponds to a closed system.

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