Detailed Balance -- from Eric Weisstein's World of Physics

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Detailed Balance

Let be the number of particles in state i, and the A and B be the Einstein coefficients. Then

(1)

In equilibrium,

(2)

(3)

But the Boltzmann distribution requires that

(4)

so

(5)

(6)

© 1996-2007 Eric W. Weisstein