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Poincaré tell us (roughly speaking) that any hamiltonian system come up arbitrarily close to the initial condition if you wait enough time.
For example, this theorem is valid for gases, and in general is one of the many key theorems that sustain Statistical Physics.
And if this theorem is valid to cosmological level , what that implies?
I mean, at the end, the universe is just evolving along the most probable line which could be one posible option of many more.