Dollars are essentially energy from physics, and trades are state transitions. So, in expectation entropy will increase. Suppose person i controls a proportion pi of the dollars. In an efficient market, entropy will be maximal, so we want to find the distribution
argmax−∑pilnpi,subject to ∑wipi=Total Societal Wealth Generation.
For a given Total Societal Wealth Generation, this is the Boltzmann distribution
pi∝eβwi
where β is the temperature (frequency of trades). I subsumed βwi as a single constant in my earlier comment to simplify matters. I was incorrect in my earlier statement; if my βwi is two higher than yours (not twice as large), I should control e2≈7 times as many dollars. I suspect some of the rise in CEO-to-worker compensation comes from β increasing, some from a less conscientious society, and some from exploitation.
Dollars are essentially energy from physics, and trades are state transitions. So, in expectation entropy will increase. Suppose person i controls a proportion pi of the dollars. In an efficient market, entropy will be maximal, so we want to find the distribution
argmax−∑pilnpi,subject to ∑wipi=Total Societal Wealth Generation.For a given Total Societal Wealth Generation, this is the Boltzmann distribution
pi∝eβwiwhere β is the temperature (frequency of trades). I subsumed βwi as a single constant in my earlier comment to simplify matters. I was incorrect in my earlier statement; if my βwi is two higher than yours (not twice as large), I should control e2≈7 times as many dollars. I suspect some of the rise in CEO-to-worker compensation comes from β increasing, some from a less conscientious society, and some from exploitation.
Isn’t $\beta$ proportional to the inverse temperature, and so should be smaller now (with easier, more frequent trading)?