Is spatially integrated entropy production useful to predict the dynamics of ecosystems?

Production of entropy by macroscopic systems in far from equilibrium as estimated from the spatial integration of entropy production density have been considered as an important concept that could help understand and predict the evolution of open systems. In this study we have used an extensive dataset of energy fluxes recorded in Ameriflux sites to compute the entropy production across different climates and ecosystems in order to analyze whether there are clear patterns showing a higher entropy production in more vegetated sites or in more developed stages. The entropy budget has been defined over a conceptualized system defined by the Earth's Critical Zone. Based on previous studies we have recognized four different formulations for the estimation of entropy production in macroscopic systems: (i) a total entropy production that accounts for all the energy fluxes including radiation fluxes, (ii) an entropy production that includes only those fluxes of energy absorbed within the open system, (iii) an entropy production that includes only living components and accounts for biochemical energy absorbed during photosynthesis and its further dissipation in the form of heat via respiration, and (iv) an entropy production that includes only incoming and outgoing heat fluxes into the open system that occurs at different temperatures. We quantified these entropy productions at different sites and stages of ecosystem development using available information recorded in 36 Ameriflux sites. We observed rather different magnitudes and patterns in all these formulations of the entropy production. Therefore, these formulations cannot be compared or considered as the same concept as has been done previously because they represent different scales and processes. In addition, we did not find a clear evidence of a maximum entropy production in more vegetated sites and at more mature stages of development, for any of these four entropy production formulations. These results suggest that hypotheses based on a maximum entropy production estimated from spatial integration over macroscopic systems in far from equilibrium should not be considered as a fundamental principle to understand or predict the evolution of these systems.