Thermal-like prior distribution

The dynamics literature has reports of a thermal-like final state distribution. This is particularly so if one examines a distribution that has only a smaller fraction of the total energy in it, most typically, a rotational distribution or a distribution in one vibration out of many. The essential difference between the prior and the Boltzmann distribution is that the prior has a sharp energy cutoff due to the conservation of the total energy. A Boltzmann distribution has an unbounded tail. Therefore the difference between the prior and a thermal distribution becomes most noticeable for states whose energies are close to the total energy limit. 

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