Balance: a thermodynamic perspective

Abstract

Balance (or evenness) as used in conventional approaches to measuring diversity needs careful definition. Nijssen et al. (Coenoses 13(1):33–38, 1998) used a mathematical approach to show that the Lorenz curve is an adequate representation of evenness and proposed that the Gini coefficient is a perfect indicator of balance. In this paper, we take an alternative thermodynamic perspective that leads to a very simple dimensionless measure of balance that ranges from 0 (perfect balance or evenness) to 1 (perfect unevenness or absolute concentration). It has the expected permutation invariance, scaling invariance, and replication invariance properties of a good evenness indicator and also has sensitivity to the transfer requirements (i.e. sensing the entropy changes correctly). It also has a naturalness property.