by Nikolai V. Shokhirev
Prof. F. Ann Walker Research Group, Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA
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Chemical systems with the same chemical composition and structure can differ in some other properties (electric dipole, spin, magnetic moment, energy, etc.). This is called that the molecule (composition, structure) can be in different states (spin, energy, etc.).
The most important parameter is energy. According to the Boltzmann law it determines the fraction of molecules in a particular state:
or normalized probabilities
Here Ej is the energy of the j-th state, kB = 1.380658 10-23 J/K is the Boltzmann constant, and T is the absolute temperature.
Remark. The probabilities are invariant with respect to the choice of energy origin.
The observed value of some quantity 
of a macroscopic system is the average value over all states:
Remark. The Boltzmann distribution gives the steady-state occupation probabilities and does not reflect any dynamic or kinetic properties including transition rates between the states.
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©Nikolai V. Shokhirev, F. Ann Walker, 2002
