Fluctuations of rates in small non-ideal reaction systems
Figure 46.4 c shows the fluctuations of the A+B reaction rate itself, which according to the formulas [139, 141] can be represented in the form
, 1 1 ( ) ( ) ( ).
U F K F Kθ θ θ θ = =
Ψ = Ψ = Ψ∑ ∑ (46.4)
In the second equality, it is taken into account that for ideal reaction systems there is no mutual influence of reagents located at different sites. The expression for the fluctuation of the function is Ψ(θAqθ
calculating fluctuations in individual areas of the surface [57, 142]:
/( ) t
U = K F , M Fθ η θΨ ∑ where the matrix product of the vector ( )B Aq q q= ,θ θ θ and the fluctuation matrix (the average of the matrix on the vector θq) are given in the parentheses.