Measuring statistical evenness: A panoramic overview

Motivated by the question “how equal is the distribution of wealth within a given human population?” economics devised an impressive toolbox of quantitative measures of societal egalitarianism including the Lorenz curve and the following indices: Gini, Pietra, Hoover, Amato, Hirschman, Theil and Atkinson. These quantitative measures-considered in the broader context of general data-sets with positive values-are, in effect, general gauges of statistical evenness. While the application of Gini’s index grew beyond economics and reached diverse fields of science, the aforementioned “evenness toolbox” has largely remained within the confines of the social sciences. The aim of this Paper is to expose this “evenness toolbox” to the physics community by presenting a comprehensive evenness-based approach to a fundamental problem in science—the measurement of statistical heterogeneity.     

The multi-agent Parrondo’s model based on the network evolution

A multi-agent Parrondo’s model is proposed in the paper. The model includes link A based on the rewiring mechanism (the network evolution) + game B (dependent on the spatial neighbors). Moreover, to produce the paradoxical effect and analyze the “agitating” effect of the network evolution, the dynamic processes of the network evolution + game B are studied. The simulation results and the theoretical analysis both show that the network evolution can make game B which is losing produce the winning paradoxical effect. Furthermore, we obtain the parameter space where the strong or weak Parrondo’s paradox occurs. Each size of the region of the parameter space is larger than the one in the available multi-agent Parrondo’s model of game A + game B. This result shows that the “agitating” effect of rewiring based on the network evolution is better than that of the zero-sum game between individuals.     

Steepest entropy increase is justified by information theory. The relations between Ziegler’s principle, Onsager’s formalism and Prigogine’s principle

Evidence for Ziegler’s principle of maximum entropy production has been accumulated from different fields such as climatic studies, crystal growth, dynamics of ecosystems and cellular metabolism. However, Ziegler’s principle is still seen with scepticism by the scientific community. The reasons for this scepticism are the absence of an accepted theoretical justification as well as the fact that Ziegler’s principle formulation seems to contradict Prigogine’s principle of minimum entropy production. In this work we aim to provide a theoretical justification for Ziegler’s principle based on information theory, which is at the basis of Gibbs’ formalism for statistical physics. Similar approaches have previously been attempted, however we believe that the justification provided here is simpler and relies in less questionable hypotheses. Once Ziegler’s principle has been formulated as a consequence of information theory, its relations with Onsager’s formulation and Prigogine’s principle are explored.