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Question: Does there exist a commutator to entropy in an uncertainty relationship?

Similar Energy and time for instance.

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    $\begingroup$ Hmm... Entropy of a system is proportional to the ln of the number of states that system can take on. But what linear operator can give you that? $\endgroup$ – Nick Jul 9 '13 at 20:19
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    $\begingroup$ Entropy is a macroscopic quantity, defined in terms of the density matrix: $S = -\text{Tr}(\rho \ln \rho)$. It doesn't have an associated Hermitian operator. Think of it as a kind of expectation value. $\endgroup$ – Benjamin Hodgson Jul 9 '13 at 20:25
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    $\begingroup$ @joshphysics - Of course! Well spotted! Unfortunately stack exchange doesn't let you edit comments after five minutes, so my mistake remains frozen as a relic for all eternity. $\endgroup$ – Benjamin Hodgson Jul 9 '13 at 20:39
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    $\begingroup$ @poorsod: Sign mistake fixed. $\endgroup$ – Qmechanic Jul 9 '13 at 21:14
  • $\begingroup$ @poorsod : $\rho$ is an hermitian operator, so $ln \rho$ and $\rho ~ ln \rho$ are hermitian operators too. $\endgroup$ – Trimok Jul 10 '13 at 10:07

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