Defining an ecological thermodynamics using discrete simulation approaches

New insights into interdisciplinary engineering endeavors, from classical modeling to nano–macroscale extrapolation and critical evaluation, weigh heavily on the pervasive nature of thermodynamics in the physical world. Just as statistical thermodynamic approaches provide a beneficial complement to a process-based macroscale thermodynamic approaches with physical systems, a Lagrangian approach to energetics in biological systems can, we believe, provide a beneficial complement to popular Eulerian approaches. Statistical thermodynamics is used as a springboard for some analogies that are similarly used to leap into the ecological scale. The Lagrangian simulation, a discrete simulation, is implemented with a spreadsheet approach, a discrete simulation approach, and a new stochastic differential equation solution approach. The Lagrangian approach complements the more widely used continuous (or Eulerian) simulation approaches such as STELLA or Environ theory approaches. The Lagrangian approach decomposes energy into small packets or ecological quanta. An ecological entropy is computed based on nodal contacts in the network, with the notion that nodal contact is analogous to molecular speed. In the cases shown, the results of ecological entropy appear generally consistent with thermodynamic entropy. A newly available simulation package (ECONET) enabled an easy Lagrangian approach to analyzing the Cone Springs and Oyster ecological models. An analogy between nodal contact numbers and molecular speed was developed to enable computation of an ecological entropy. There is a similarity between classical and ecological entropy based on similarity in shape of the Maxwell–Boltzmann distributions to the packet-nodal contact numbers. An ecological temperature can be defined based on this similarity. Selected ratios of ecological entropy versus classical macroscopic entropy appeared to have some degree of robustness. Other aspects of ecological thermodynamics remain to be developed. It is felt that the ecological thermodynamics approach presented offers an improved way to combine biochemical and ecological entropy. A sound combination of entropies at multiple scales will help bring together measurements at disparate scales.