Employing entropy to study growth and resilience in systems

A study by researchers from the IIASA Advanced Systems Analysis Program, explored the relation between entropy-based indicators describing system efficiency and redundancy, and system growth and resilience to shocks. In another study they suggested ways to incorporate the properties of non-equilibrium and path-dependency into the traditional notion of entropy to better describe real-life human-earth systems.

Entropy is a concept that links the microscopic world with macroscopic (systemic) phenomena and defines the degree of disorder in a system. It was first introduced in physics to relate the velocities of particles (microscopic world) with temperature (macroscopic property). It is useful for describing and analyzing various complex systems consisting of a large number of interacting elements, where the concern of decision makers is on macroscopic parameters, while dynamics unfold at the micro-level of individual elements. In a closed system, entropy will always increase, while open systems, including all environmental and social systems, are able to manage the rate of entropy generation to some degree by maintaining a network structure.

Many real-life complex systems are networked systems. Food webs, for example, are networks of species feeding on one another, supply chains are networks of firms supplying intermediate goods to each other, and social systems are networks of people exchanging information and opinions–to name just a few. In systems, where the number of network elements is large and the connections are subject to so many factors that they can be seen as random to some degree, the concept of (information) entropy becomes applicable.

The study analyzed global commodity trade using the information entropy concept [1]. Its complex network structure arises from bilateral and multilateral trade agreements. The researchers found that trade agreements can make commodity trade networks more efficient and lead to more rapid growth in the volume of trade. However, these gains come at the expense of resilience to economic shocks, such as the 2009 global financial crisis, which decimated economies around the world. Perhaps counter intuitively, the results also showed that networks that had greater redundancies did not have to sacrifice growth.

Since complex systems are highly interconnected, traditional Gaussian statistics is not applicable to them. The statistics of complex systems is the statistics of power laws, where large and extreme events appear much more often than Gaussian statistics predicts. In earlier research [2], IIASA researchers suggested a way to extend the notion of entropy to systems that are networked and history dependent, to make it more applicable to complex human-earth systems. In this study, they showed that simple path-dependent systems, such as situations with a winner-takes-all dynamic, can indeed be studied by means of developed generalized entropy. Winner-takes-all dynamics appear in many socioeconomic and environmental contexts, which show strong reinforcement and hence “fat tailed” distributions. This in turn implies that catastrophic events with high impacts happen more often than common sense suggests.

References

[1] Kharrazi A, Rovenskaya E, & Fath BD (2017). Network structure impacts global commodity trade growth and resilience. PLoS ONE 12 (2): e0171184

[2] Thurner S, Corominas-Murtra B, & Hanel R (2017). Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle. Physical Review E 96 (3)