Boltzmanns H-teorem

The master equation describes the transition rate out of the state r:

The entropy is


By differentiation


By switching r and s

By addition


If
s > r

then
ln(s) > ln(t)

This yields the SL-IV form of the second law:

0

The system evolves towards a unique equilibrium state. This state is easily found from

= 0

which shows that in the equilibrium state r is constant, independent of r.

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Author Per Stoltze stoltze@fysik.dtu.dk