Diversity as an entropic measure derived from entropiclike functionals

We present two derivations of an entropy-related function known as diversity in terms of entropy functionals. In the first case, we express diversity as an exponential of the difference between two forms of Shannon entropy. In the second case, the Jensen-Shannon divergence, an entropic function, only depends on diversity. Then, in the second part of this work, we apply diversity and Shannon entropy to a system in equilibrium (Ising model) and also to an out-of-equilibrium system (seismic region in Alaska). It turns out that diversity gives sharper responses at the critical points and more texture in the general trends.