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Title: Nonequilibrium Entropy in a Shock

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:
ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
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.
Margolin, Len G. Nonequilibrium Entropy in a Shock. United States. doi:10.3390/e19070368.
Margolin, Len G. 2017. "Nonequilibrium Entropy in a Shock". United States. doi:10.3390/e19070368. https://www.osti.gov/servlets/purl/1398924.
@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}
}