In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation is where is the diffusion coefficient; is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, ; is the Boltzmann constant; is the absolute temperature. This equation is an early example of a fluctuation-dissipation relation. Two frequently used important special forms of the relation are: Einstein–Smoluchowski equation, for diffusion of charged particles: Stokes–Einstein equation, for diffusion of spherical particles through a liquid with low Reynolds number: Here is the electrical charge of a particle; is the electrical mobility of the charged particle; is the dynamic viscosity; is the radius of the spherical particle. Special cases Electrical mobility equation For a particle with electrical charge , its electrical mobility is related to its generalized mobility by the equation . The parameter is the ratio of the particle's terminal drift velocity to an applied electric field. Hence, the equation in the case of a charged particle is given as where is the diffusion coefficient (). is the electrical mobility (). is the electric charge of particle (C, coulombs) is the electron temperature or ion temperature in plasma (K). If the temperature is given in Volt, which is more common for plasma: where is the Charge number of particle (unitless) is electron temperature or ion temperature in plasma (V). Stokes–Einstein equation In the limit of low Reynolds number, the mobility μ is the inverse of the drag coefficient . A damping constant is frequently used for the inverse momentum relaxation time (time needed for the inertia momentum to become negligible compared to the random momenta) of the diffusive object. For spherical particles of radius r, Stokes' law gives where is the viscosity of the medium. Thus the Einstein–Smoluchowski relation results into the Stokes–Einstein relation This has been applied for many years to estimating the self-diffusion coefficient in liquids, and a version consistent with isomorph theory has been confirmed by computer simulations of the Lennard-Jones system. In the case of rotational diffusion, the friction is , and the rotational diffusion constant is This is sometimes referred to as the Stokes–Einstein–Debye relation. Semiconductor In a semiconductor with an arbitrary density of states, i.e.