Einstein Relation (kinetic Theory)

Einstein Relation (kinetic Theory)

In physics (specifically, in kinetic theory) the Einstein relation (also known as Einstein–Smoluchowski relation) is a previously unexpected connection revealed independently by Albert Einstein in 1905 and by Marian Smoluchowski in 1906 in their papers on Brownian motion. The more general form of the equation is


  • D is the diffusion constant;
  • μ is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, μ = vd / F;
  • kB is Boltzmann's constant;
  • T is the absolute temperature.

This equation is an early example of a fluctuation-dissipation relation.

Two frequently used important special cases of the relation are:

(Electrical mobility equation, for diffusion of charged particles)
("Stokes-Einstein equation", for diffusion of spherical particles through liquid with low Reynolds number)


  • q is the electrical charge of a particle;
  • μq, the electrical mobility of the charged particle;
  • η is viscosity;
  • r is the radius of the spherical particle.

Read more about Einstein Relation (kinetic Theory):  Proof of General Case

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Einstein Relation (kinetic Theory) - Proof of General Case
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