Wealth Distribution: A Boltzmann-inspired Perspective

Yesterday, I talked with a client about Boltzmann's distribution and how it changes with temperature. Today, I had fun making an animation with ChatGPT to show how the distribution shifts as temperature increases. In the animation, the X-axis represents the velocity of N2 gas, and the Y-axis shows probability. Different colors represent the distribution at different temperatures.


As temperature rises, the distribution becomes broader. The right-hand side, representing higher velocities, extends further with increasing temperature.


I thought about relating this to the real world. Instead of velocity, I considered wealth, and instead of temperature, I thought about the wealth of nations. Developing countries aim to push their population towards the right side of the curve, where people transition from poverty to the middle class, and then to self-sufficiency and prosperity. In an ideal society, we need a single narrow peak at the right-hand side of the graph. But that will never be achieved, so realistically, a narrow distribution without a long tail is acceptable. 


Just like molecules gain energy with each collision, some individuals gain wealth through opportunities and hard work, ending up as ultra-rich. But they're a small fraction compared to the majority.


It's the government's job to ensure people stay within a certain range of distribution and prevent extreme wealth concentration. Taxing the ultra-rich more helps maintain balance.


Yet, it's essential to have some deviation to motivate people to strive for more. Many factors, like tax evasion, can distort our perception of where we stand in the distribution.


It's also evident from the distribution that the increasing wealth of a country would reduce the number of people on the left-hand side (poverty) and make overall growth possible. Developed countries typically have lower crime rates and more opportunities for their citizens to thrive. This highlights the importance of economic prosperity in creating a stable and prosperous society.


This analogy offers a new perspective on wealth distribution and government policies. It's a simple way to understand complex socioeconomic issues.


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