The above example illustrates a simplified version of Schrodinger ratio assessment as a thermodynamic orien-tor. Since a comprehensive description of the ecological succession requires a more accurate set of ecosystem attributes and thermodynamic characters, revised versions of the Schrodinger ratio have been calculated and proposed in the literature.
According to Ludovisi, calculation of the Schrodinger ratio for ecological systems only makes sense for self-organizing elements of an ecosystem, which essentially belong to the biological component. In this case, the ratio is given by
T e prod
where S bprod is the entropy produced by biological processes and Exb is the exergy embodied in the living biomass. The ratio is an indicator of the capacity of b biological communities to exploit incoming low-entropy energy to maintain their organization.
This revised version of the Schrodinger ratio, namely the specific entropy production or specific dissipation of a system, has been calculated by Ludovisi for lake ecosystems. With respect to the classical ratio stated by Odum, it provides a deeper insight into the development status of an ecosystem along the trophic gradient. The ratio R/B only considers respiration in assessing the rate of entropy dissipation (ignoring processes such as anaerobic decomposition and photosynthesis) and biomass in assessing structural entropy (ignoring the entropy production and exergy functions).
In Ludovisi's case studies of shallow lakes ranging from oligotrophic to hypereutrophic, specific entropy production is calculated as the ratio of biological entropy production in lake ecosystems to chemical, or better, ecological exergy. Biological entropy production can be calculated from meteorological (solar radiation, albedo, and temperature of water surface) and hydrological (water transparency, total phosphorus, and chlorophyll concentration) data. Monthly values of biological entropy production in lakes turn out to be largely due to plankton, which predominates over other biological contributions. The ratio is therefore calculated as the ratio of entropy production by the plankton community to exergy stored in the plankton biomass.
Certain findings support the hypothesis that extensive thermodynamic quantities, such as entropy production and exergy, that depend on environmental conditions (such as availability of trophic resources), can be used as indicators of ecosystem maturity. For instance, trends of specific dissipation by plankton can be investigated during different seasons and years and the effects of changes in an entropy flow (e.g., associated with radiation or exchange of heat and matter) on ecosystem function can be observed. Human perturbations, such as water pollution, wastewater loading, and thermal alterations, can also be included in the entropy balance and their effects on the ecosystem estimated. The results of application of this ratio to lake ecosystems in the literature confirm the hypothesis of entropy trends in ecosystem evolution: entropy production is higher during intermediate stages of development of a community, when organisms colonize an unexploited environment. Maximum entropy production is reached immediately before the climax 'summer' phytoplankton community.
Specific dissipation seems more apt for measuring ecosystem maturity (the ecological distance covered by an ecosystem under given environmental constraints) than exergy or biological entropy production (which is a measure of biological activity) per se, because it combines the two extensive functions in a way that translates the ecological strategy adopted by organisms, which is one of the most significant criteria for evaluating ecosystem maturity, into thermodynamic terms. Thus specific dissipation seems to have the requisites of a primary thermodynamic orientor of ecosystem evolution.
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