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Is it necessarily true that a quantum-mechanical system in thermal equilibrium is in a mixed state? If so, why is this the case? Is there any physical intuition as to why one cannot use a pure state description?

I've been told statements such as "thermal fluctuations in the system make it impossible to obtain a complete (and hence pure state) description of it", and "a many-body system in equilibrium necessarily exhibits decoherence and hence cannot be described by a pure state". However, I'm unsure whether these are correct, and if they are, how to interpret them intuitively.

Any help on this matter would be much appreciated.

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    $\begingroup$ Using a pure state description would imply that you know exactly which microstate the system is in, which usually isn't the case in thermodynamics. $\endgroup$ – probably_someone Jul 9 '18 at 21:33
  • $\begingroup$ @probably_someone Is there some physical intuition as to why this is the case? Is it always true that a quantum many-body system in thermal equilibrium will be in a mixed state? $\endgroup$ – Will Jul 9 '18 at 21:37
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    $\begingroup$ For what it’s worth this is true even in classical thermodynamics. If you know the temperature and volume of an ideal gas, there is a ton you don’t know. Being able to proceed without this detailed microscopic information is the whole point of thermodynamics. $\endgroup$ – knzhou Jul 9 '18 at 21:43
  • $\begingroup$ One way of interpreting a mixed state is that there is a classical, as well as a quantum uncertainty. This is exactly what you would expect for a thermal state described by statistical mechanics. $\endgroup$ – By Symmetry Jul 9 '18 at 21:44
  • $\begingroup$ @BySymmetry Why is it necessarily the case that a thermal state has classical uncertainty though? Where is the information loss? $\endgroup$ – Will Jul 9 '18 at 21:52

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