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Non-equilibrium Thermodynamics and Statistical MechanicsFoundations and Applications$
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Phil Attard

Print publication date: 2012

Print ISBN-13: 9780199662760

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199662760.001.0001

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Second Entropy for Fluctuating Hydrodynamics

Second Entropy for Fluctuating Hydrodynamics

Chapter:
(p.121) Chapter 5 Second Entropy for Fluctuating Hydrodynamics
Source:
Non-equilibrium Thermodynamics and Statistical Mechanics
Author(s):

Phil Attard

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199662760.003.0005

The second entropy for fluctuating hydrodynamics is maximised to obtain the equations of hydrodynamics (Navier-Stokes, energy, mass flow). The approach is an extension of the Landau and Lifshitz theory of fluctuating hydrodynamics. The derivation invokes the material conservation laws; the mass, energy, and momentum fluxes; and the entropy of the system in the presence of convective flows; expressions for all of these are derived and explained. Chemical reactions are included. The coupling of the fluxes and the transport coefficients are identified from the Curie symmetry principle. A variational formulation for hydrodynamics is given in which the second entropy is to be maximised with respect to both structure and flux.

Keywords:   hydrodynamics, Navier-Stokes, variational, convection, chemical reaction, flux

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