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
where 'sqrt()' represents a square root, "k" is Boltzmann's constant and "T" is the temperature in Kelvin.

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