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:
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)
“There is a relation between the hours of our life and the centuries of time. As the air I breathe is drawn from the great repositories of nature, as the light on my book is yielded by a star a hundred millions of miles distant, as the poise of my body depends on the equilibrium of centrifugal and centripetal forces, so the hours should be instructed by the ages and the ages explained by the hours.”
—Ralph Waldo Emerson (1803–1882)