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arXiv · 1511.06176

Quantum Thermodynamics, Entropy of the Universe, Free Energy, and the Second Law

George L. Barnes·Phillip C. Lotshaw·Michael E. Kellman
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Abstract

We take the view that the standard von Neumann definition, in which the entropy $S^{vN}$ of a pure state is zero, is in evident conflict with the statement of the second law that the entropy of the universe $S_{univ}$ increases in spontaneous processes, $ ΔS_{univ} > 0$. Here we seek an alternative entropy of the universe $S_{univ}$ that is in accord with the second law, in a spirit not dissimilar to von Neumann himself in lesser-known work. We perform simulations of time dependent dynamics for a previously developed \cite{polyadbath} model quantum system becoming entangled with a quantum environment. We test the new definition of the entropy of the system-environment "universe" against the standard thermodynamic relation $ ΔF_{sys} = - T ΔS_{univ} $, calculating system properties using the reduced density matrix and standard von Neumann entropy. Good agreement is obtained, showing the compatibility of an entropy for a pure state of a universe with the statement of the second law and the concept of free energy. Interesting deviation from microcanonical behavior within the zero order energy shell is observed in a context of effectively microcanonical behavior within the much larger total basis of the time dependent universe.

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George L. Barnes, Phillip C. Lotshaw, Michael E. Kellman. 2018-10-24. Quantum Thermodynamics, Entropy of the Universe, Free Energy, and the Second Law. https://arxiv.org/abs/1511.06176

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