Sociological and Economic Inequality and the Second Law

The paper presents a solution to a mathematical problem namely; what will be the distribution function of P particles in N boxes when all the different possible configurations of particles and boxes have an equal probability. (Usually the assumption is that there is an equal probability to any box). The obtained distribution function yields an uneven number of particles in the boxes. It seems that this distribution fits well many observed distributions such as the distribution of economic wealth. The uneven distribution of wealth is attributed today to mechanisms of "the riches get richer". Here it is suggested that the wealth inequality might be a mere unbiased probabilistic effect. This distribution predicts that the richest box out of an ensemble of a million boxes (sharing a large number of particles), will posses 5% of the wealth, more then the wealth of the poorest 100,000 boxes together. This distribution, which is analogues to a thermal equilibrium distribution, may be a basis to a definition of an entopical economic equilibrium. In addition it can tell us how far is an economic system from equilibrium. The fit of this distribution to the results of polls and opinion surveys of economic and social as well as political (election to the Knesset) domains is remarkable as demonstrated in (reference to graphs). It seems that a random distribution of particles in two boxes is not necessarily 50:50.