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
Famous quotes containing the words einstein and/or relation:
“God is subtle, but he is not malicious.
[Raffiniert ist der Herr Gott, aber boshaft ist er nicht.]”
—Albert Einstein (1879–1955)
“Concord is just as idiotic as ever in relation to the spirits and their knockings. Most people here believe in a spiritual world ... in spirits which the very bullfrogs in our meadows would blackball. Their evil genius is seeing how low it can degrade them. The hooting of owls, the croaking of frogs, is celestial wisdom in comparison.”
—Henry David Thoreau (1817–1862)