Nonequilibrium Entropy in a Shock

doi:10.3390/e19070368

Title: Nonequilibrium Entropy in a Shock

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In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies the Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.

Authors:

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: 2017-07-19

Report Number(s):: LA-UR-17-24413
Journal ID: ISSN 1099-4300; ENTRFG

Grant/Contract Number:: AC52-06NA25396

Type:: Accepted Manuscript

Journal Name:: Entropy

Additional Journal Information:: Journal Volume: 19; Journal Issue: 7; Journal ID: ISSN 1099-4300

Publisher:: MDPI

Research Org:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org:: USDOE Laboratory Directed Research and Development (LDRD) Program

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; shocks; nonequilibrium thermodynamics; entropy

OSTI Identifier:: 1398924


                    Margolin, Len G. Nonequilibrium Entropy in a Shock.  United States: N. p.,  
        Web.  doi:10.3390/e19070368.

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                    Margolin, Len G. Nonequilibrium Entropy in a Shock.  United States.  doi:10.3390/e19070368.

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                    Margolin, Len G. 2017.  
        "Nonequilibrium Entropy in a Shock".  United States.  
        doi:10.3390/e19070368.  https://www.osti.gov/servlets/purl/1398924.

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@article{osti_1398924,

  title        = {Nonequilibrium Entropy in a Shock},

  author       = {Margolin, Len G.},

  abstractNote = {In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies the Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.},

  doi          = {10.3390/e19070368},

  journal      = {Entropy},

  number       = 7,

  volume       = 19,

  place        = {United States},

  year         = {2017},

  month        = {7}

}

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Free Publicly Accessible Full Text
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10.3390/e19070368
https://doi.org/10.3390/e19070368

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Title: Nonequilibrium Entropy in a Shock

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