Ecological pyramid of dissipation function and entropy production in aquatic ecosystems

Abstract

Food chain and food web have been, thus far, depicted by number of individuals, matter (biomass) and energy, but not by the concept concerning to the second law of thermodynamics. The present paper takes up three U.S. mid-Atlantic estuaries and delineates marine trophic structure in the term of the concept of this missing link: the second law of thermodynamics. Homeostatic structure and function of living systems is maintained by chemical, physical and organic activities in biotic systems. These activities are supported by chemical energy released by decomposition of macromolecules in organisms by oxygen incorporated from the outside (respiration). This chemical energy finally becomes heat energy and is discarded to the outside. This heat energy is dissipation function in thermodynamics, and dissipation function divided by absolute temperature of organism–water is entropy production. As example, mid-Atlantic estuaries on the eastern U.S. coast are analyzed, based on the study of (Monaco, M.E., Ulanowicz, R.E., 1997. Comparative ecosystem trophic structure of three U.S. mid-Atlantic estuaries. Mar. Ecol. Prog. Ser. 161, 239–254). They give 13–14 trophic compartments in each estuaries, and respiration and other characteristic quantities for each trophic compartments. Trophic position of compartment in each estuary is adopted and arranged in accord to the food web diagrams of (Monaco, M.E., Ulanowicz, R.E., 1997. Comparative ecosystem trophic structure of three U.S. mid-Atlantic estuaries. Mar. Ecol. Prog. Ser. 161, 239–254). Plots of trophic number versus respiration become of half-pyramid shape, which is also applied to dissipation function because respiration is equal to dissipation function in thermodynamics. Annual average temperature at average depth in Narragansett estuary is, for example, 10.0 °C (=283.2 K). The difference between maximum and minimum temperature at averaged depth is 14.2 °C (=287.4 K). This difference is small compared with the absolute temperature scale. Hence let us make an approximation that the temperature of the water body of this estuary is about constant and uniform over a year and 10.0 °C = 283.2 K. Entropy production is obtained by dividing dissipation function by this value. Pattern of trophic position versus entropy production multiplied by the temperature is of similar shape to dissipation function: half-pyramid. Other two estuaries show similar results.