Ginzburg Criterion: Why Choose Volumes of Correlation Length?

[wdlang]

indeed, the fluctuations should be smaller than the average value of the order parameter

but why choose a volume with size of the correlation length?

why cannot we choose a larger volume? as the volume increases, surely the fluctuations will

decreases relative to the average value

 

[AJS2011]

but why choose a volume with size of the correlation length?

If your question is in the context of superconductivity then:

The coherence length is the "natural scale" set by parameters of GL equation. Likewise the penetration depth sets a "natural scale" for phenomena related to EM field. For example if the size of your system is much less than penetration depth you can forget about the presence of EM field. The same argument for your question.