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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