# commutator to entropy in an uncertainty relationship?

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

Similar Energy and time for instance.

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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? –  Nick Jul 9 '13 at 20:19
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. –  Benjamin Hodgson Jul 9 '13 at 20:25
@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. –  Benjamin Hodgson Jul 9 '13 at 20:39
@poorsod: Sign mistake fixed. –  Qmechanic Jul 9 '13 at 21:14
@Qmechanic: thanks! –  Benjamin Hodgson Jul 9 '13 at 21:36