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The Second Law of Thermodynamics states that the entropy of the Universe must increase. When we look a the Cosmic Microwave Background Radiation we see that the early Universe was in thermal equilibrium, which corresponds to a state of maximum entropy. How is it then that the entropy of the Universe is increasing? How is the Second Law consistent with our observations of the CMB?

(Edited for typos)

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While the contents of the universe were in nearly perfect thermal equilibrium back then, there was another factor that brought them out of equilibrium: gravity. Being very evenly distributed is a low-entropy state as gravity is concerned. Entropy increases if matter is allowed to clump together, releasing potential energy and creating all sorts of inhomogenities that further disequilibrate the contents. The total entropy has been increasing thanks to an increase of the gravitational part of the entropy, despite the matter/energy contribution becoming somewhat less entropic.

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  • $\begingroup$ Actually I thought that one of the argumenst for the inflation era of the universe is that it could not be in thermal equillibrium with classical thermodynamics, though the CMB shows great uniformity and the same black body no matter where one looks in the sky. $\endgroup$ – anna v May 7 '18 at 19:00
  • $\begingroup$ It is the post-inflationary Hubble patch that was in thermal equilibrium and hence had low entropy. $\endgroup$ – bapowell May 7 '18 at 20:01
  • $\begingroup$ @ Anders Sandberg So, you're saying that that concentration of matter which is due to gravity (rather than that part of such a concentration which might have occurred anyway, due to random motion) tends to equalize the temperature of matter in general? It's a little hard to picture, because collisions, even if they would not have occurred at all without gravitation, must nevertheless tend to concentrate heat at the surfaces or points of the bodies entering into contact, rather than distributing it more evenly thru their combined mass. What am I missing here? Is "random motion" unjustified? $\endgroup$ – Edouard Dec 1 '19 at 16:17
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    $\begingroup$ @Edouard - No, gravity does not equalize temperatures. Quite the opposite: it heats up the matter that is collapsing into heavier objects, and other forces like electromagnetism has to disperse the heat. The entropy of clumpy matter is higher than for evenly spread matter. $\endgroup$ – Anders Sandberg Dec 2 '19 at 2:31

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