What is a Maxwell-Boltzmann Distribution?
A Maxwell-Boltzmann Distribution is a probability distribution used for describing the speeds of various particles within a stationary container at a specific temperature. The distribution is often represented with a graph, with the y-axis defined as the number of molecules and the x-axis defined as the speed. In short, the graph shows the number of molecules per unit speed. Derivations of the distribution have been conceptualized as well, including Maxwell-Boltzmann statistics, which emphasizes statistical thermodynamics.
How does the Maxwell-Boltzmann Distribution work?
Understanding the Distribution
When looking at the distribution on a graph, it is important to note that the curve skews to the left. There is a longer tail on right end of the graph as speed increases, and accordingly ends on the left at zero, as no molecule can be traveling at a speed less than zero. Furthermore, one may infer that the peak of the curve is the average speed of the gas, however it actually represents the most probable speed, and the average speed is actually located more to the right of the peak. Because the tail of the graph extends further on the right of the peak than the left, it makes sense that the average would be offset to the right of the distribution's peak.
Maxwell-Boltzmann Distributions and Machine Learning
There is a specialized form of neural network known as a Boltzmann machine. The machine is an unsupervised deep learning model that primarily is used to better understand the impact of complex parameters like entropy and thermodynamics. Because the machine learns the parameters, patterns, and correlations between points in the data, the machine is deemed to be a model of unsupervised learning. The model is then used to monitor and study abnormalities in behavior based upon its training data.