The Evolution of Complexity and Interestingness in Physical Systems

The evolution of physical systems often exhibits a fascinating pattern: complexity and interestingness increase over time, reach a peak, and then decline. This behavior contrasts with the monotonic increase of entropy, as dictated by the second law of thermodynamics. To understand this dichotomy, we must delve into the concepts of complexity, interestingness, and entropy, and explore their interplay in the natural world.

Understanding Complexity and Interestingness

Complexity refers to the degree of intricacy or the number of components and interactions within a system. A highly complex system has many interconnected parts that exhibit intricate behaviors and relationships. Interestingness, although subjective, typically relates to the novelty, unpredictability, and richness of patterns within a system. Systems that exhibit surprising and non-trivial behaviors are often deemed more interesting.

The Role of Entropy

Entropy is a measure of disorder or randomness in a system. According to the second law of thermodynamics, the entropy of an isolated system never decreases; it either increases or remains constant. This law underpins the idea that physical systems naturally evolve towards states of higher disorder.

The Interplay Between Complexity, Interestingness, and Entropy

Initially, as a system evolves, its complexity and interestingness tend to increase. This is because the system explores various configurations, leading to the emergence of intricate structures and novel behaviors. For instance, in the early stages of the universe, simple particles combined to form atoms, molecules, stars, and eventually complex structures like galaxies and life forms.

As the system continues to evolve, it reaches a point where complexity and interestingness peak. This peak represents a state where the system exhibits the highest degree of structured complexity and the most intriguing patterns. At this stage, the system has a balance of order and randomness that maximizes its interestingness.

However, as entropy continues to increase, the system begins to decay. The high-energy states and intricate structures gradually give way to more disordered and less interesting configurations. For example, stars burn out, biological systems age, and organized structures eventually break down. The decline in complexity and interestingness corresponds to the system’s progression towards thermodynamic equilibrium, a state of maximum entropy and minimal organization.

Real-World Examples

  1. Cosmic Evolution: The universe started with the Big Bang, a highly disordered state. Over billions of years, matter coalesced into stars, galaxies, and planetary systems, increasing the complexity and interestingness. Eventually, stars will exhaust their fuel, leading to a decrease in complexity as the universe moves towards heat death, characterized by maximum entropy.
  2. Biological Systems: Life on Earth evolved from simple single-celled organisms to complex multicellular life forms, peaking in diversity and complexity. Over time, individual organisms and ecosystems age and decay, reducing their complexity as they succumb to the inexorable increase in entropy.
  3. Technological Systems: Human-made systems, such as software or mechanical devices, start with simple designs that evolve into highly complex and sophisticated forms. Over time, wear and tear, obsolescence, and lack of maintenance lead to a decline in their functionality and complexity.


The observed pattern of increasing and then decreasing complexity and interestingness in physical systems, contrasted with the monotonic rise of entropy, highlights the dynamic nature of evolution and decay. Complexity and interestingness reach their zenith when a system strikes a balance between order and chaos. As entropy continues to rise, this balance tips towards greater disorder, leading to the eventual decline in the system’s complexity and interestingness. This interplay underscores the transient nature of structured complexity in an ever-evolving universe governed by the laws of thermodynamics.

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