Min-Max principle of entropy production with time in aquatic communities

Abstract

The study of entropy is important for understanding essential nature of complex and functional systems from thermodynamic viewpoint. However, entropy content of living systems cannot be estimated both by experiment and by calculation. On the contrary, entropy production has been evaluated for plants, animals, human bodies and lake-ecosystems. The present paper provides entropy production for aquatic communities using data of respiration in aquatic food webs. Oxygen-uptake by respiration in organisms decomposes macromolecules such as carbohydrate, protein and lipid and liberates chemical energy, which is then used to chemical reactions and motions of matter in organisms to support lively order in structure and function in organisms. Finally, this chemical energy becomes heat energy and discarded to the outside (dissipation function). Accompanying this heat energy, entropy production which inevitably occurs by irreversibility also discarded to the outside. Here, dissipation function and entropy production are estimated from data of respiration. Both specific dissipation function and specific entropy production in aquatic communities become two-phase character with respect to trophic diversity: early increase and later decrease with the increase of trophic diversity. The trophic diversity in these aquatic ecosystems is shown to be positively correlated with the degree of eutrophication, and the degree of eutrophication is “arrow of time” in the hierarchy of aquatic ecosystems. Hence, specific dissipation function and specific entropy production have the two-phase: early increase and later decrease with “time”. This two-directional tendency with time may be characterized as “Biological Principle” in contrast to “Physical Principle” (variation principle) that is always one-directional.