Chapter

Fluctuation Theory

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/9780199662760.003.0002
Fluctuation Theory

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Fluctuation theory is used to introduce non-equilibrium thermodynamics. Fluctuations in macrostates are described by Gaussian probabilities and a quadratic form for the second or transition entropy. From a small time expansion for both Markov and non-Markov systems, the Onsager regression hypothesis and reciprocal relations for the transport coefficients emerge. Computer simulation results for the fluctuation in the first energy moment are used to illustrate the nature of thermodynamic regression. The analysis is extended to mixed parity states. The very important reduction condition on the second entropy, and the relation between the second entropy coefficients and the time correlation function, are established.

Keywords: fluctuation; Gaussian; Onsager; reciprocal relation; regression; transport coefficient; time correlation

Chapter.  13952 words.  Illustrated.

Subjects: Condensed Matter Physics

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