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Fluctuations Notes

Fluctuations Notes - From the discussion of fluctuations in...

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From the discussion of fluctuations in the number of particles on the left side of the box, or coin flips, we found in lecture: " N L ( ) 2 = N L 2 # N L 2 N L = h i i = 1 N $ " N L ( ) 2 = h i h j j = 1 N $ i = 1 N $ # h i i = 1 N $ h j j = 1 N $ At this point, we used the statistical independence of the particles to eliminate all terms where i j: h i h j = h i h j for i " j At this point, we are left with only terms where i = j, thus we eliminate one of the
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