Gravitational potential energy equation to deduce Maxwell-Boltzmann distribution

For a long time, I have been interested in the normal distribution discovered by mathematician Gauss. There are also occasional applications in practical work. It is psychologically understandable that everything in nature is normally distributed, but it is not clear about its physical or philosophical essence. According to the article [1] (DOI 10.5281/zenodo. 4569171) " Perfect Universe Theory with Infinite Layers of Nesting and Differentiability", the complete momentum can be obtained by deriving the complete energy from the velocity, and the gravitational potential energy can be obtained by deriving the high-order term of the complete momentum from the velocity and multiplying by 2. The essence of these formulas are some special distribution functions. I found that the essence of the energy flow distribution is to replace v / c in the gravitational potential energy distribution with the square of v /c, and the energy flow distribution can be simplified to the standard normal distribution when the energy growth effect is ignored in the low-speed macroscopic condition. Considering the relationship between the potential energy and the average kinetic energy of the ideal gas in the closed volume, the Maxwell-Boltzmann distribution can be obtained. The gravitational potential energy distribution in this paper is a special gamma distribution whose domain of definition is extended to (- ∞, + ∞). The information entropy of gamma distribution defined on (0, + ∞) is positive, and the information entropy of gamma distribution defined on (- ∞, 0) is negative. The average value of the two is 1, which indicates that the universe is a whole and confirms the traditional Chinese Taoism philosophy of "the unity of human and nature".