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Quantum Approach to a Derivation of the Second Law of Thermodynamics

Jochen Gemmer·Alexander Otte·Guenter Mahler
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Abstract

We re-interprete the microcanonical conditions in the quantum domain as constraints for the interaction of the "gas-subsystem" under consideration and its environment ("container"). The time-average of a purity-measure is found to equal the average over the respective path in Hilbert-space. We then show that for typical (degenerate or non-degenerate) thermodynamical systems almost all states within the allowed region of Hilbert-space have a local von Neumann-entropy S close to the maximum and a purity P close to its minimum, respectively. Typically thermodynamical systems should therefore obey the second law.

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Jochen Gemmer, Alexander Otte, Guenter Mahler. 2001-01-30. Quantum Approach to a Derivation of the Second Law of Thermodynamics. https://doi.org/10.1103/physrevlett.86.1927

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