11. This screening causes a Boltzmann distribution of electrons to form around the electric potentials. 12. Sampling from generic probabilistic models, such as a Boltzmann distribution , is hard. 13. The parametrised normalizing constant for the Boltzmann distribution plays a central role in statistical mechanics. 14. In the first approximation, it is thus simply given by the Boltzmann distribution law: 15. However, in such a case, there is no antiderivative for Boltzmann distribution function. 16. Because of this Boltzmann distribution can be used to solve a very wide variety of problems. 17. In more general mathematical settings, the Boltzmann distribution is also known as the Gibbs measure. 18. If the charge density follows a Boltzmann distribution , then the Poisson-Boltzmann equation results. 19. Which agrees with the Boltzmann distribution . 20. Figure 2 shows the Maxwell Boltzmann distribution for the speeds of the atoms in four noble gases.
