The work expended is f x , where x is the total displacement during the time. The particle's displacement has a mean part due to the external dragging, and a varying part due to its own diffusion, so σ σ x 2 = 2 D t , where D is the diffusion coefficient. Together, we obtain f = k B T D E [ x ] / t or γ γ D = k B T , where γ γ is the viscosity. This is the fluctuation-dissipation theorem.