Bose-Einstein Condensation in Competitive Processes

Abstract

We introduce an irreversible discrete multiplicative process that undergoes Bose-Einstein condensation as a generic model of competition. New players with different abilities successively join the game and compete for limited resources. A player's future gain is proportional to its ability and its current gain. The theory provides three principles for this type of competition: competitive exclusion, punctuated equilibria, and a critical condition for the distribution of the players' abilities necessary for the dominance and the evolution. We apply this theory to genetics, ecology and economy.