Fluctuation theorem and Green-Kubo relations

Journal of Chemical Physics

Volumn 112, Issue 22, 2000, Pages 9727-9735

  Searles, Debra J ^a   Evans, Denis J ^b  

^a GRIFFITH UNIVERSITY   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

MOLECULAR DYNAMICS; THERMODYNAMICS; TRANSPORT PROPERTIES;

FLUCTUATION THEOREM; GREEN-KUBO RELATIONS;

PHYSICAL CHEMISTRY;

EID: 0033718224     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.481610     Document Type: Article

References (26)

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17. CLT states that under quite general conditions (Refs. 13, 14), the mean of an infinite set of independent variables is normally distributed, independent of the distribution of the individual independent variables. However, for a finite number of variables, unless the independent variables are distributed as a Gaussian, the sum will show some deviation from a Gaussian and the relative error in the deviation will generally increase with the number of standard deviations from the mean when the number of variables is large (Refs. 13, 14).
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20. Note that a Gaussian distribution does not imply a FT. The FT is a much stronger statement: it specifies the relationship between the mean and the standard deviation if the distribution is Gaussian. We note that the FT, of course, does not require the distribution to be Gaussian.
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25. We assume that the FT and Eqs. (23) and (30) have reached their limiting behavior at that time.
26. A similar argument can be used if we take the thermodynamic limit, in which the distribution collapses onto a delta function at the mean. In this case a GK expression is valid for large systems provided the distribution of the time-averaged fluxes is Gaussian at a minimal volume.