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.