Metabolic Dynamics of Ecosystems Realizing Steady Log-Uniform Distributions: The Case of Commodities in Shops.

From the viewpoint of statistical physics, ecosystems in the real world are very attractive targets of research as examples of far-from thermal equilibrium systems where various kinds of components are coming in and out continuously while keeping the whole systems quasi-stationary. As a fortunate example of a fully-observable ecosystem, we analyzed the comprehensive data of convenience stores where approximately 5% of the commodity species is replaced by new ones daily. The share of stores for each species fluctuates significantly; however, the entire distribution of shares is fairly stationary and follows the log-uniform distribution, that is, the power law distribution with exponent 0.