# Can entanglement be used to decrease entropy of two systems?

I know that entanglement can create correlation between systems. Would it be true to say that entanglement create constraints between systems? Can constraints be used to lower the total entropy of systems?

In other words, say we have two separate systems with certain entropy values. If we create some kind of interaction between the two systems and did so without investing energy, would it be possible to create constraints between the two systems such that the total entropy decreases?

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## 1 Answer

Entanglement decreases the entropy of two systems combined as opposed to separately, and this is the accepted definition of the amount of entanglement. The amount of entanglement/correlation of two quantum systems is the sum of the entropy of each system in isolated minus the entropy in the combined density matrix. This includes both entanglement and classical correlation together, but it works when the full system is in a pure state, in which case it is a pure measure of entanglement.

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Hmm I see. Does this imply that you can violate the second law of thermodynamics using entanglement? –  Uri Jul 8 '12 at 0:12
@Uri: Not unless you have a machine that sets up entanglement without producing entropy. To set up entanglement requires emitting entropy in a greater amount than you get from the entanglement just by conservation of entropy. There is no magic entanglement device that produces entangled states without emitting heat. –  Ron Maimon Jul 8 '12 at 7:03
I really believed for a moment that I had come up with this. So I just came on the site a moment ago...and wrote a question...didn't need to check as I done it myself. And then from corner of my eye I saw this question and screamed why why why. Then I come here and get told it's the accepted definition so now i'm going out to find some worms to eat –  Lucy Meadow May 4 at 15:08