Quantifying the Relationship between Inequality and the Stability and Sustainability of the Coupled Societal-Environmental System in New Orleans

Shruti Singh, BT Werner and Dylan McNamara

Diagnosing and quantifying the unstable, unsustainable relationship between present day societies and the environment largely remains a difficult scientific and urgently practical challenge. We propose that societies exhibit a form of societal dissipation analogous to energy dissipation in physics (where coherent motion at the macroscopic scale is transformed into stochastic motion of molecules, as in frictional heating), and that this societal dissipation plays a key role in stabilizing societal-environmental interactions. This hypothesis is investigated using a numerical model of development and flooding in New Orleans. River and hurricane storm-surge-induced floods, flood damage to structures, agent-based market interactions describing port services, hotels and home building, labor relations and levee construction are simulated geographically on a cellular domain. A dynamical analysis of the model reveals that wealth energy (square of the time derivative of wealth) is a conserved quantity that can be tracked as it flows in and out of the model domain and amongst owner, laborer and government agents; and that societal dissipation can be measured as the transfer via wages of domain-level, profit-generating wealth energy of owner agents to labor agents at the level of individual cells. Stability is quantified using the volume of phase space enclosed by system excursions in response to flood-induced perturbations. A baseline version of the model reproduces the historical development and levee-height increases of New Orleans. Two modifications are investigated: (1) wages are depressed and laborer housing density is increased artificially, corresponding to labor repression and, in the limit, slavery; and (2) labor requirements are reduced artificially, corresponding to productivity increases and automation. For these cases, stability and sustainability decrease and inequality between owner and laborer agents increases. Stability and sustainability monotonically decrease with increasing inequality and societal dissipation.