Schrodinger Ratio Assessment The RB Ratio

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Howard Odum interpreted the Schrodinger ratio from an entropy point of view, considering that exportation of entropy produced by metabolic processes (respiration) enabled maintenance of the low-entropy content of biological systems (their incorporated biomass). Thus, the Schrodinger ratio was calculated in terms of entropy production and entropy content.

Case studies in the literature have regarded respiration of ecosystems as the major dissipative process (generation—dissipation entropy balance) and biomass (the total content of organic matter) as a measure of the entropy of structure. According to the maximum biomass principle, Odum states that ecological succession culminates in a stabilized ecosystem in which maximum biomass is maintained per unit of energy flow. Thus, the Schrodinger ratio is calculated as the ratio of respiration to structural biomass, considering only the biotic component of the ecosystem. If the energy flows are divided by temperature, an entropy variation is obtained. This ratio describes the entropy-generation rate necessary to maintain a low-entropy structure relative to its surroundings:

Sprod Entropy generation rate Respiration/ T

(So-S) Entropy of structure Free energy stored/ T Respiration Biomass

This version of the Schrodinger ratio is also known as the R/B ratio. Values of this ratio at different times give information about ecosystem evolution through a succession of biological states and provide an overview of system behavior over its lifetime. The ratio is intended as an indicator of the developmental status of ecological systems or even ecosystem maturity. For instance, the ratio R/B tends to be lower for highly structured, near-climax ecosystems than for less complex, less mature ecosystems. It tends to decrease in the course of ecological succession. It has also been regarded as a thermodynamic orientor which should be a minimum throughout ecosystem development.

According to Odum natural forests invest energy in structure and diversity by capturing solar energy, recycling, and generating high gross production. The energy increase due to structure and diversity may be estimated in terms of gross production (energy is used by ecosystems to maximize gross productivity and achieve maximum power). The energy required to maintain structure and diversity is supplied by respiration. The change in entropy is the energy flow of maintenance respiration divided by the Kelvin temperature. As practical example, he drew up a balance of the entropy production and entropy content of a forest. Considering the energy used to maximize the structure and diversity of the forest in terms of gross production, the change in entropy was

Respiration 103kcalm 2d 1 T ~ 295deg

The entropy content of forest structure is derived from the energy stored as biomass:

Biomass 170 000 kcal m - 2

295 deg

576 kcal deg 1m

The Schrodinger ratio of the forest is

Entropy generation rate Respiration 0.349 Entropy of structure Biomass 576 = 0.00061 d-1

which is the general environmental entropy increase required to maintain the low-entropy structure and diversity of the forest. It is observed that higher temperatures cause greater depreciation but also affect maintenance metabolic rates.

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