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I have problem with uderstanding of Liouville equation. Which sais that if we have a

Hamiltonian system (energy is conserved), then the the volume of phase space is

conserved, or equivalently the probability density is conserved (the total derivative

of probability density per time is 0).

On the other hand, and isolated hamiltonian system is going to an equilibrium state,

where the probability density is the same for all state in phase space.

How can system reach the equilibrium, when the probaility density is on the develpment

trajectory conserved and at the begining is not the same for all state?

Thaks a lot!