Open Problems in Interplay between QM & 2nd Law of Thermodynamics?

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Geremia
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What are some open problems in the interplay between Quantum Mechanics and the 2nd Law of Thermodynamics?

thanks
 
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2nd law can be proved just fine via statistical physics, both in classical and quantum mechanics. For the latter you use thermal ensemble density matrices as states and the Liouville equation as their time evolution equation. In both cases (classical and qm) the entropy is a property of the macroscopic ensemble description of a physical system and behaves at it should.
 
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