The CDF for the

Boltzmann distribution maybe approximated by means of the new special function [T.sub.[kappa],[mu]](x) as follows:

While LTE is established within the plasma, the population at different levels is governed by the

Boltzmann distribution law.

While the intensity, depending on

Boltzmann distribution if the plasma at local thermal equilibrium, can be described as [3]

where [alpha], [beta] = x, y, z are tensor index, [OMEGA] is the volume of the unit cell, [f.sub.0] is the

Boltzmann distribution function, and [[sigma].sub.[alpha][beta]](e) is defined as

[C.sub.c] for the

Boltzmann Distribution in One Dimension.

The author has organized the main body of his text in seven chapters and six appendices devoted to energy and entropy, entropy and free energy, the evaporation of a liquid drop, gases and the basics of thermodynamics, mixtures and reactions, phases and temperature variations, heat dispersion and temperature, the

Boltzmann distribution law, and a wide variety of other related subjects.

To further illustrate the described procedures, [N.sub.2] in an equilibrium

Boltzmann distribution was chosen as a test case because its potential energy function is well known from high-resolution spectroscopic measurements.

Further approximations applied throughout this work are the assumption of a

Boltzmann distribution of the excited level population and the ideal gas law.

introduced a fractional Fokker-Planck equation (FFPE) which was shown to obey generalized Einstein relations, and its stationary solution is the

Boltzmann distribution [1].

A special way of assigning probabilities to values is the

Boltzmann distribution proposed by Sutton, defined as

The above distribution is called the

Boltzmann distribution (or Gibbs distribution), and was introduced in the context of the random generation of combinatorial objects by Douchon, Flajolet, Louchard and Schaeffer in 2004, see (4).