Macrostates of classical stochastic systems

Journal of Chemical Physics

Volumn 105, Issue 22, 1996, Pages 9986-10007

  Shalloway, David ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008910807     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.472830     Document Type: Article

References (49)

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4. α (old).
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22. In quantum mechanics ψ would be called a "state function," but we do not use this term to avoid confusion with its thermodynamic meaning. 23 Without loss of generality we assume that there are no infinite potential barriers that dissect the space into completely disconnected subregions. (This would induce degenerate eigenfunctions with zero relaxation rates.) If this were the case, each subregion could be analyzed independently.
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24. Throughout the paper, subscripted Greek letters identify macrostates and bear no relationship to regular Greek letters such as the inverse temperature β. Summations over these macrostate indices are over all m macrostates.
25. b.
26. 0〉 provides an alternative measure of the "information" content of the macrostate description, although its experimental interpretation is not as clear as that of Y.
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28. n≥m terms in eigenfunction expansion (12), since the truncated expansion would not, in general, be positive semi-definite as required for a physical reduced distribution. In contrast, this property is guaranteed by Eq. (31).
29. obs and F are identical since the matrices are similar.
30. 0 does not satisfy normalization condition (16), and thus is proportional to, but is not itself, a reduced distribution.
31. We explicitly display only time dependence within bra-ket vectors; the dependence on β and R is implicit.
32. The equivalence of the integral and differential forms of the equations is proven in Appendix A of Ref. 4.
33. The determinant in Eq. (59) is irrelevant to the characteristic packet equations. It is included so that Eqs. (62) and (66) will be satisfied.
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39. Equations (84) assumes that η points out of macrostate region a.
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