Why equal opportunities lead to maximum inequality? The wealth condensation paradox generally solved

If wealthier people have advantages in having higher returns than the poor, inequality will unequivocally increase. But is equal opportunity enough to prevent it? According to our results, no. We prove that fair markets lead to the inevitable concentration of wealth. It is an intrinsic feature of its non-trivial dynamics, even though no individual can have the advantages of repeated gains. We solve this apparent paradox by presenting a rigorous analytical proof. Using the Boltzmann-like master equation formalism, we demonstrate that a fair market that gives each agent the same expected return leads the system to maximum inequality, i.e. the thermal death of the economy. Therefore, even equality of opportunity –without an explicit bias in favor of wealthy people– generates inequality.