Energy-level molecular system design, quantum

For a sample of many molecules, under the assumption of no interaction between them, the probabilities are directly proportional to the numbers of molecules in each state, the populations, which we designate as n. For a large collection of A molecules at some temperature T, the number found in the ith energy level of an A molecule is n = NPj, where N is the total number of A molecules. Is it possible for a large collection of molecules to have populations of molecular quantum states other than those dictated by the Maxwell-Boltzmann law Yes. But in that event, the system is not at equilibrium, which means that it is not stable and is undergoing change. The distribution law holds for equilibrium conditions, and under those conditions, it can be used to determine the number of molecules in particular energy level states. 

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