Chapter

Statistical mechanics

D. Violeau

in Fluid Mechanics and the SPH Method

Published in print May 2012 | ISBN: 9780199655526
Published online September 2012 | e-ISBN: 9780191741227 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199655526.003.0002
Statistical mechanics

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The notions of Chapter 1 are extended here to systems of many individuals (thus many degrees of freedom), now seen from a statistical viewpoint. In the phase space, the chapter shows Liouville’s theorem of volume preservation and deduce the Boltzmann equation for the probability density of molecular velocities. The chapter then introduces the statistical concepts of entropy and temperature, and prove that the entropy increases (H-Theorem). Thermodynamical quantities are deduced. Finally, dissipative systems are treated, the energy being transferred from large scales to small scales, i.e. from macroscopic to internal energy. Friction forces are introduced from Onsager’s theory of kinetic coefficients, and these concepts are applied to dissipative forces in a system of macroscopic particles. Lastly, fluctuations are considered in the Fokker–Plank formalism.

Keywords: Liouville’s theorem; Boltzmann equation; entropy; kinetic coefficients; dissipative forces

Chapter.  34951 words.  Illustrated.

Subjects: Condensed Matter Physics

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