This article shows that the entropy in a free market is maximized under the allocative efficiency condition. In contrast to that, it is shown that any pre-determined allocation, as it is the case with the collection and distribution of taxes, exhibits a higher probability of minimizing the entropy in the system, where the loss in entropy corresponds to the deadweight loss caused by the excess burden of taxation. The implications are that any chaotic system, or exchange economy, converges to an optimal structure of wealth distribution which maximizes social welfare, in contrast to a randomly, pre-determined distribution of wealth.
