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

where

  • 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)

where

  • 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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