The Mathematics of Sustainable Energy Analysis:
Forcing a New Paradigm of Sustainability Research
John Schramski, Assistant Professor
Low Energy Systems Research Program
Environmental Engineering, University of Georgia
Ecosystem modeling, in particular, ecological network analysis (ENA) is a growing mathematically
intense field of sustainability research. At the confluence of modeling, graph, ecosystem, and general
systems theory coupled together with a diverse range of mathematics, ENA is providing the holistic
perspective necessary for sustainability science. However, consider that when mass and energy
ecological network models are compared, the internal cycling of energy models is less than the
internal cycling of mass models (nitrogen, water, phosphorous, etc.). This is due to the second law of
thermodynamics where energy is significantly less useful at every transaction (eventually all low
quality heat energy is radiated back to space). As such, although vital, the margins of extra energy
afforded the ecosystem during this cycling are slim. However, for anthropocentric energy systems,
when we attempt to develop models and their corresponding mathematics, we discover essentially no
networks and thus, no cycling. Energy usage in anthropocentric systems is primarily linear and short;
we use it once and the waste heat is subsequently dissipated.
The future energy crisis coupled with our observations of ecosystem functionality with regard to
energy call for a new research model that develops ecosystem-like networks of highly efficient
anthropocentric energy use. We accomplish this by pursuing the mathematics of network analysis for
urban sustainable energy planning. In our theoretical modeling, we remove excess energy (in our
case, we remove fossil and nuclear fuels) to force sufficiently slim margins of waste which then forces
ecosystem-like cycling of energy where we can then begin network mapping the anthropocentric
energy systems. We find that the basis of such an anthropocentric ecosystem-like energy model
canonically begins with a society’s agroecological food supply system. The energy output of the local
farming operation must be greater than the energy input (e.g., one farmer supporting seven others) for
the community to generate excess energy (e.g., biomass, beasts of burden, human labor) to be
routed/cycled for community development (e.g., schools, hospitals). Along with a discussion of these
observations, this work details the initial theoretical input-output sustainable farming model, which
forms the basis of our anthropocentric energy network model construction.