A
fundamental result in
statistical physics which links
microscopic (thermal)
fluctuations with the
macroscopic property that creates a
drag force on a
particle in a medium.
Browninan motion is often expressed using a particle on which two distinct forces act:
ma=-g x v(t) + f x G(t),
where "g" is the drag force when the particle has velocity "v(t)" and "f" is a constant that dictates the influence of the zero-mean (usually Gaussian white) noise component "G(t)".
However, and this is the point of this theorem, the drag force is dependent on the noise component and thermodynamic consistency requires that
f=sqrt(2*g*k*T),
where 'sqrt()' represents a square root, "k" is Boltzmann's constant and "T" is the temperature in Kelvin.