Quantum Microcanonical Entropy, Boltzmann's Equation, and the Second Law

Phillip C. Lotshaw; Michael E. Kellman

doi:10.1021/acs.jpca.8b10666

Quantum Microcanonical Entropy, Boltzmann's Equation, and the Second Law

Phillip C. Lotshaw, Michael E. Kellman

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A recent proposal for a quantum entropy Suniv_Q for a pure state of a system-environment "universe" is developed to encompass a much more realistic temperature bath. Microcanonical entropy is formulated in the context of the idea of a quantum microcanonical shell. The fundamental relation that holds for the classical microcanonical ensemble -TΔS_univ = ΔF_sys is tested for the quantum entropy ΔSuniv_Q in numerical simulations. It is found that there is "excess entropy production" ΔS^x due to quantum time-energy uncertainty and spreading of states in the zero-order basis. The excess entropy production is found numerically to become small as the magnitude of the system-environment coupling nears zero, as one would hope for in the limit of the classical microcanonical ensemble. The quantum microcanonical ensemble and the new "universe entropy" thereby appear as well-founded concepts poised to serve as a point of departure for time-dependent processes in which excess entropy production is physically significant.

Original language	English
Pages (from-to)	831-840
Number of pages	10
Journal	Journal of Physical Chemistry A
Volume	123
Issue number	4
DOIs	https://doi.org/10.1021/acs.jpca.8b10666
State	Published - Jan 31 2019
Externally published	Yes

Funding

This work was supported by the U.S. Department of Energy Basic Energy Sciences program under Contract DE-FG02-05ER15634. We would like to thank Benjamıń Alemań, Dietrich Belitz, Jeff Cina, and John Toner for stimulating discussions. M.K. especially thanks David Perry for stimulating discussions about the Shannon entropy and quantum thermodynamics. P.L. thanks Rob Yelle and Craig Rasmussen for technical assistance on computations and George Barnes for the original version of the code developed in this work. This work benefited from access to the University of Oregon high performance computers, ACISS and Talapas.

Funders	Funder number
Basic Energy Sciences	DE-FG02-05ER15634

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10.1021/acs.jpca.8b10666

Cite this

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Quantum Microcanonical Entropy, Boltzmann's Equation, and the Second Law

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