Interpretation

• Right-hand side is macroscopic property

  • applicable at macroscopic time scales

• For any given configuration, each atom represents a point of high concentration (a weak fluctuation)

• View left-hand side of formula as the movement of this atom

  • ensemble average over all initial conditions
  • asymptotic linear behavior of mean-square displacement gives diffusion constant
  • independent data can be collected for each molecule

Slope here gives D

Einstein equation

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