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.