Some biological and social systems grow more complex over time—and stay that way.

One example of this over evolutionary timescales is the rise of self-replicating RNA molecules from simple organic compounds during life’s early history on Earth. Another is the gradual development of eusocial behavior in ants and bees. Examples over shorter timescales include urbanization, technological advances, and crowd dynamics.

However, most naturally occurring systems—impelled by the second law of thermodynamics—actually become less complex over time. (An egg falling off a table and splattering on the floor is the standard example - all internal structure, all of its complexity, gets lost in the splatter.)

We wish to answer the questions, “What is it about a system that determines whether it grows more complex or less complex over time? What do highly complex systems like economies and ecosystems have in common?

One possible answer involves natural selection, which is a very common complexity-increasing process. However many biological systems increase in complexity through other processes (e.g., through the processes of neutral evolution, or embryogenesis). Moreover, some increases in social complexity occur much too rapidly to be driven by natural selection. So a deeper understanding of natural selection’s relation to complexity cannot fully answer our questions.

Our goal is to use real-world examples of complex systems — both biological and social — to motivate several formal definitions of complexity, and then use them to investigate what features are common to all processes that drive complexity increases through time.

We use information theory as a scientific bridge connecting the thermodynamic properties of systems to the dynamics of their complexity. In this way we aim to provide more a complete answer to our questions.