Measuring Social Complexity and the Emergence of Cooperation from Entropic Principles. The Collapse of Rapa Nui as a Case Study

The quantitative assessment of the state and dynamics of a social system is a very difficult problem. This issue is important for both practical and theoretical reasons such as establishing the efficiency of social action programs, detecting possible community needs or allocating resources. In this paper we propose a new general theoretical framework for the study of social complexity, based on the relation of complexity and entropy in combination with evolutionary dynamics to assess the dynamics of the system. Imposing the second law of thermodynamics, we study the conditions under which cooperation emerges and demonstrate that it depends on the relative importance of local and global fitness. As cooperation is a central concept in sustainability, this thermodynamic-informational approach allows new insights and means to assess it using the concept of Helmholtz free energy. We then introduce a new set of equations that consider the more general case where the social system changes both in time and space, and relate our findings to sustainability. Finally we present a model for the collapse of Rapa Nui island civilization in NetLogo. We applied our approach to measure both the entropy production and the complexity of the system and the results support our purpose that sustainability needs a positive entropy production regime which is related to cooperation emergence.