by Nikolai V. Shokhirev

Prof. F. Ann Walker
Research Group,
Department of Chemistry,
University of Arizona,
Tucson, Arizona 85721, USA

### Boltzmann law

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 *E*_{j} is the energy of the j-th state, *k*_{B} =
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.

©Nikolai V. Shokhirev, F. Ann Walker, 2002