The nature of matter and energy exchange of an ecological process defines the applicability of the thermodynamic functions for describing an ecosystem. A plant community is an open system consisting of living species as material components. Following the basic laws of thermodynamics, the enthalpy H stored in biomass form of a plant community will be related to its total equivalent biomass quantity CT, the weighted average standard chemical potential μ0, Gibbs free energy G, entropy S and temperature T by H = G + TS = CTμ0. Using h, f and s to denote H/(RT), G/(RT) and S/R (R denoting the gas constant), respectively, the conventional function can be transformed to h = f + s = CTμ0/(RT). The relation sm/CT = SIm = ln(N) derived from the maximal discrete entropy theorem shows that sm (the maximum s) and SIm (the maximum information entropy) will increase with increase in the total number of species N, suggesting that N has an upper limit Nm subject to regional species resource. As an upper limt of SI and s/CT, ln(N) is applied as a biodiversity index. As an upper limt of ln(N), ln(Nm) can thus be regarded as a biodiversity potential index as it takes into account the available number of species distributed in the surrounding areas of the plant community, showing the potential limit for further increase in its biodiversity. The difference between ln(Nm) and ln(N) dtermines the distribution of H as G and TS, indicating that the internal energy distribution of an acosystem is a function of its productivity and biodiversity. The potential trends of increasing N towards Nm and increasing s towards sm suggest that an ecosystem can possess natural trends towards increase in both its species richness and evenness.

The experimental data used for testing the applicability of the thermodynamic equations presented in the theoretical section were obtained from an ecological restoration project implemented at a manganese tailing site. Restoration of the plant community was shown to be an irreversible process characterized by spontaneous increases in its total biomass CT and total number of plant species N associated with increases in its enthalpy H, Gibbs free energy G and entropy S. Species enrichment was the cause for the decease in mass ratio xi (biomass of a species Ci divided by CT) and biomass growth potential μi (the partial derivative of Gi with respect to Ci). The increase in s/CT (s denoting the ratio of S to gas constant R) associated with decrease in f/CT (f denoting the ratio of G to RT) with increasing N confirmed that the restored plant community possessed natural trends towards increase in its species richness and evenness. The observed trends gave support to use of the thermodynamic functions for describing the productivity-biodiversity relationship. The present analysis did not fully prove the use of the Shannon form of information entropy as a biodiversity index for the investigated plant communities. Because of the presence of significant differences in individuals among species, the biodiversity of the plant community could not be uniquely determined by its individual numbers. In comparison, the entropy factor s was shown to be a suitable biodiversity index. The fact that N is the key factor that determines the changes in s/CT and f/CT makes △N > 0 a useful index for determining the direction of spontaneous changes for all open systems with continuous input of matter and energy. As a measure of disorder, s can be generally applied as a diversity index for all systems involving transformations of matter and energy.

The data used in the analysis were obtained from an ecologically restored plant community. The basic idea presented in this study is that the conventionally defined chemical potential μi can be used as a growth potential index for a species for evaluating the biotic effect on its realized niche. An ecological niche defines a suitable environment for a species to live while μi defines the adaptability of a species to a given environment. The deviation from the fundamental niche of a plant species due to changes in its living environment will thus be reflected by the changes in its μi value. The μi factor is a function of μi0 (the standard chemical potential) and N (the species number). Similar to the fundamental niche, μi0 is uniquely determined by abiotic factors. Increasing N will reduce μi and thus, similar to the realized niche, μi takes into account the biotic effect.