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When a box of nitrogen with an entropy of 1 is mixed with a box of oxygen with an entropy of also 1 then you get a box with an entropy of 3. Perhaps a bit simplified but why is always the total entropy of two joint boxes bigger than the sum of the entropy of the boxes?

And the same is valid for colliding black holes. When two BH of the same size are collided you get a BH with an entropy which is bigger than the sum of the entropy of the singel BH. What causes this and is the reason for this the same as in the first example above?

Marijn
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  • Some relevant answers found here – fffred Dec 06 '16 at 17:50
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    Lazy pointer to Wikipedia’s “Entropy of mixing” page – Frédéric Grosshans Dec 06 '16 at 17:51
  • Thanks for the references ,but is it possible to explain this in a bit more logically layman terms? And if the entropy of the whole system is raised, so does the temperature? – Marijn Dec 06 '16 at 18:44
  • Entropy is basically confusion. If you mix two boxes you get more confusion than the original sum of their respective randomness. Likewise for black holes: you merge two equal mass ones and you double the Schwarzschild radius, and so quadruple the area of the horizon. – Cosmas Zachos Dec 06 '16 at 19:25
  • Even there is no interaction between nitrogen and oxygen, the mixture entropy cannot be 2. For example if the volume of oxygen box is 9 times larger than the volume of the nitrogen box. The nitrogen entropy will increase from 1 to 10 by itself because its micro state increases by 10 times. – user115350 Dec 07 '16 at 02:19

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