A non–extensive thermodynamic theory of ecological systems

After almost 30 years of development, it is not controversial issue that the so–called Tsallis entropy provides a useful approach to studying the complexity where the non–additivity of the systems under consideration is frequently met. Also, in the ecological research, Tsallis entropy, or in other words, q–entropy has been found itself as a generalized approach to define a range of diversity indices including Shannon–Wiener and Simpson indices. As a further stage of development in theoretical research, a thermodynamic theory based on Tsallis entropy or diversity indices in ecology has to be constructed for ecological systems to provide knowledge of ecological macroscopic behaviors. The standard method of theoretical physics is used in the manipulation and the equivalence between phenomenological thermodynamics and ecological aspects is the purpose of the ongoing research.

The present work is in the line of the authors research to implement Tsallis non–extensivity approach to obtain the most important thermodynamic quantities of ecological systems such as internal energy U_q and temperature T_q based on a given modeled truncated Boltzmann distribution of the Whittaker plot for a dataset. These quantities have their own ecological meaning, especially the temperature T_q provides the insight of equilibrium condition among ecological systems as it is well–known in 0th law of thermodynamics.