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Entropy measures the number of microscopic states of a given system.

For a pure state, the count is one. Thus, entropy ~ log(1) = zero.

However, on the other hand, if we calculate the entropy of finding a particle in real space. It will not be zero. pure state entropy paradox

My question is, what is the entropy of such pure state? Is it zero or not? Then what about my idea to calculate it in real space distribution?

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  • $\begingroup$ What's your question? $\endgroup$
    – Shivam Sarodia
    Commented Apr 2, 2014 at 22:52
  • $\begingroup$ My question is, what is the entropy of such pure state? Is it zero or not? Then what about my idea to calculate it in real space distribution? $\endgroup$
    – Jian
    Commented Apr 2, 2014 at 23:02
  • $\begingroup$ Is this paradox occurs because the "subsystem" of your division is invalid or because they are correlated? I am not sure. $\endgroup$
    – an offer can't refuse
    Commented Apr 4, 2014 at 5:29

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The new divided four boxes are not a complete basis. Quantum states have more information than real position distributions.

The pure state is zero entropy. Although we still have some sort of uncertainty on position, this uncertainty comes purely from the quantum uncertainty, which can never be known, thus entropy does not include this term.

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