Chapter

Second Entropy for Fluctuating Hydrodynamics

Phil Attard

in Non-equilibrium Thermodynamics and Statistical Mechanics

Published in print October 2012 | ISBN: 9780199662760
Published online January 2013 | e-ISBN: 9780191745287 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199662760.003.0005
Second Entropy for Fluctuating Hydrodynamics

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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

Chapter.  12421 words. 

Subjects: Condensed Matter Physics

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