This miniseries expands on the concepts introduced in our prior 5 part miniseries “The Power of Process” by delving deeper into the mechanics of Complex Adaptive Systems (CAS). It uncovers the intricate processes behind system evolution, exploring core principles like boundaries, symmetry breaking, iterative rules, and entropy. The series reveals how these forces shape the complexity observed in everything from natural ecosystems to financial markets. By emphasizing the interconnectedness and structured nature of systems, it provides a comprehensive view of how the universe evolves, offering profound insights into growth, adaptation, and eventual decline.

Part 5/6: Entropy and the Driving Force Behind Complex Adaptive Systems

In this instalment of our miniseries on Complex Adaptive Systems (CAS), we dive deeper into the forces that underpin the evolution, growth, and eventual decay of all systems. In our previous discussions, we explored how systems are shaped by boundaries, symmetry breaking, and iterative rules that create the framework for complexity. But what powers this constant evolution? What drives systems forward through time, ensuring that they grow, adapt, and inevitably decline?

The answer lies in one of the fundamental principles of thermodynamics: entropy. As we explore in this post, entropy provides the energy that drives the time-asymmetric processes that govern system evolution. Drawing on the works of thinkers like Peter Atkins, who described systems as ratchets for entropy in his book The Laws of Thermodynamics, and Erwin Schrödinger, who explained the relationship between life and entropy in What is Life?, we will unravel how entropy plays a central role in the dynamism of complex systems. This post will also explain why all subsystems, from living organisms to financial markets, are inherently ephemeral in nature—subject to the natural cycle of growth and decay dictated by entropy.

Entropy: The Engine Behind Time-Asymmetry in Systems

Entropy is a measure of disorder or randomness within a system, and in the context of complex adaptive systems, it is the fundamental driver of time asymmetry—why systems naturally evolve in a particular direction. This concept is grounded in the second law of thermodynamics, which states that the total entropy of a closed system can never decrease; it only increases over time. This explains why processes in the universe are irreversible and naturally flow in one direction—forward.

However, most systems we observe, from biological organisms and ecosystems to financial markets, are open systems that interact with their environment. These systems are not truly closed, as they take in energy, matter, or information from their surroundings, which allows them to locally reduce entropy, at least temporarily, by creating order within themselves. For example, living organisms consume low-entropy food and release higher-entropy waste, thereby maintaining their internal structure while contributing to the overall increase in entropy of the universe.

This concept of how open systems sustain themselves in the face of entropy was explored in depth by British chemist and physicist Peter Atkins in his book The Laws of Thermodynamics: A Very Short Introduction. Atkins was a professor of chemistry at the University of Oxford and is well-known for his work in explaining complex scientific principles in an accessible way. In his book, Atkins describes how open systems, like living organisms or ecosystems, act like “entropy ratchets.” These systems resist the natural drift toward disorder by continually exporting entropy to their surroundings, much like a ratchet mechanism that allows movement in one direction while preventing it from going backward.

However, as Atkins points out, this resistance to entropy is temporary. Over time, all systems, no matter how ordered, eventually succumb to the larger forces of entropy, leading to their decay or transformation as they exhaust their energy reserves.

Entropy and Time-Asymmetry: An Example from Nature

To illustrate this, consider a forest ecosystem. Plants, as part of this system, take in low-entropy energy from sunlight, converting it into ordered structures like leaves and branches through photosynthesis. Animals feed on these plants, maintaining order within their own bodies by consuming the plant’s stored energy. Yet, as energy is transferred through the food chain, waste products are produced, and energy is lost as heat, contributing to the overall increase in entropy in the universe.

While the forest ecosystem creates temporary order, it cannot escape the arrow of time driven by entropy. Over time, even the most well-maintained organism within the system will eventually decay, returning its matter to the environment as it decomposes. This decomposition process releases nutrients back into the soil, contributing to the next cycle of life, and further illustrates how systems move forward in time due to entropic forces.

Boundaries, Scale Invariance, and Entropy: Balancing Energy and Complexity

Boundaries and scale invariance both play critical roles in how entropy unfolds within complex systems, particularly by setting limits on how energy flows and how complex patterns emerge. As systems scale up, their boundaries create points where scale invariance adapts or breaks, impacting how energy is distributed and consumed.

Take the example of metabolic rates in animals. Smaller animals, like hummingbirds, have high surface-area-to-volume ratios, requiring intense metabolic energy to maintain body heat. As animals increase in size, their metabolism scales sub-linearly: larger animals, like elephants, use energy more efficiently to prevent overheating and reduce metabolic demands. This boundary in scaling—where size limits energy needs—ensures the animal’s internal order remains sustainable and protects it from entropy-induced breakdown. This metabolic adjustment represents a boundary condition that reconciles scale with entropy.

In ecosystems, boundaries often arise naturally, creating regions where energy flow and entropy rates vary. Forest layers, for example, separate high-energy canopy areas from low-energy understory zones. The energy-intensive canopy absorbs the most sunlight, fostering rapid growth and competition, while the shaded understory supports slower-growing species adapted to low-light conditions. These natural boundaries manage energy flow across the ecosystem, balancing entropy between high- and low-energy regions. Without these boundaries, energy distribution would be uneven, likely destabilizing the system’s structure and leading to overconsumption or collapse.

In geological systems, mountain ranges provide a boundary between energy dynamics on either side of the range. On the windward side, precipitation supports lush growth and soil renewal, while the leeward side experiences arid conditions due to the rain shadow effect. This boundary creates distinct regions where energy and entropy unfold differently, allowing distinct ecosystems to emerge based on scale- and boundary-driven energy flows. The scale and terrain constraints set by mountains impose limits on plant and animal adaptation, requiring each side to balance entropy uniquely.

The interplay between boundaries, scale invariance, and entropy underscores how complex systems manage growth and maintain stability. As systems scale up, boundaries adjust how energy flows and entropy unfolds, ensuring that the system remains organized despite increasing complexity. This principle emphasizes that while scale invariance allows for efficient patterns, boundaries are essential for managing the entropy that scales bring.

Entropy in Financial Markets

Financial markets also exhibit entropic behavior. At times, order and structure are created through the flow of capital and information, leading to the emergence of trends or patterns. However, markets are not immune to disorder; they are subject to volatility, market shocks, and information asymmetry, all of which increase the system’s overall entropy. Traders and financial systems may attempt to create temporary pockets of order by predicting trends or managing risk, but over time, these markets, like ecosystems, are driven toward disorder as market conditions change and inefficiencies arise.

Peter Atkins’ work helps us understand that entropy is the driving force behind these processes, propelling systems forward in time and creating the irreversible cycles of growth, decay, and transformation. While open systems may temporarily resist entropy by interacting with their environment, they cannot escape the broader trend toward disorder that governs the universe. In this way, whether in ecosystems, financial markets, or other adaptive systems, entropy is the underlying mechanism that shapes their evolution.

Entropy in Financial Markets: Rethinking Per Capita Perspectives

In financial markets, per capita metrics often aim to simplify the system’s dynamics by averaging effects across participants. While this can offer insight into individual contributions, it frequently misrepresents the cumulative effects of entropy across interconnected financial networks. The interconnected nature of market actors—where institutional investors, high-frequency traders, and retail investors each play unique roles—creates a complex web where entropy-driven disruptions have far-reaching impacts. Per capita perspectives overlook these variations, flattening out the intense, compounding influences certain entities can exert on market stability and volatility.

Consider the 2008 financial crisis. While average investment losses per individual might provide a basic understanding of the financial impact, it fails to capture the broader entropy effects that led to systemic collapse. Institutional players contributed disproportionate risk through high-leverage assets, creating feedback loops that intensified the crisis. Per capita metrics obscure these high-risk dynamics by treating the market as if each participant’s impact was identical. However, the true entropy in the system—fueled by these concentrated risks—unfolded through cumulative, interconnected effects that magnified instability.

In high-frequency trading (HFT), per capita averages miss the amplifying impact these trades have on market entropy. HFT transactions happen in microseconds, creating ripple effects that standard metrics cannot accurately capture. Their speed and volume introduce substantial entropy into the market, which spreads across the system through price volatility and liquidity shocks. By focusing on per capita measures, such metrics fail to account for these non-linear, rapid accumulations of entropy that define the market’s behavior under high HFT activity.

Additionally, market bubbles exemplify how per capita views can miss entropy’s cumulative impact. As prices inflate, optimism spreads contagiously, creating herding behavior that inflates prices further. When bubbles burst, entropy spreads rapidly, but per capita metrics obscure the disproportional losses suffered by those who entered later in the cycle or held more speculative assets. These cumulative, interconnected entropy effects are crucial for understanding market dynamics, emphasizing the need for a systemic view that looks beyond per capita figures.

By examining entropy in financial markets through a systemic lens, we gain a clearer view of how interconnected actions and cumulative risks contribute to market volatility and resilience. Moving beyond per capita metrics allows us to grasp the true nature of market entropy, reflecting the system’s capacity for abrupt, non-linear changes.

Boundaries and Symmetry Breaking: The Framework for Evolution

As we have explored, boundaries and symmetry breaking are critical to the development of complexity in CAS. Boundaries define where a system begins and ends, regulating the exchange of energy between the system and its environment. For example, a biological cell’s membrane maintains internal order while allowing nutrients and waste to pass in and out, thus maintaining the flow of low-entropy resources into the system.

Symmetry breaking—the process that shifts systems from homogeneity to differentiation—plays a crucial role in determining how entropy drives system evolution. In What is Life?, Schrödinger argued that life temporarily avoids the fate of increasing disorder by feeding on negative entropy (or negentropy). He saw life as an entropic anomaly: while the universe trends toward disorder, living systems maintain order by constantly importing energy from their environment. Symmetry breaking allows for differentiation, creating complexity by introducing new opportunities for energy exchange and adaptation.

When symmetry breaks, systems develop distinct patterns and behaviors, driven by the iterative rules discussed in previous posts. These rules guide systems to evolve in a time-asymmetric manner, shaped by the increasing entropy in the surrounding environment. Boundaries and symmetry breaking define the path of evolution, but it is entropy that supplies the driving force that keeps systems moving forward.

Life, Death, Growth, and Decline: The Natural Cycle of Subsystems

While boundaries and symmetry breaking set the stage for how systems evolve and develop complexity, entropy continues to play a defining role as systems pass through the phases of growth, stability, and, eventually, decline. Just as boundaries regulate energy exchange and symmetry breaking fosters differentiation, the ongoing influence of entropy dictates the inevitable life cycle of every subsystem.

No system can grow or maintain complexity indefinitely. Entropy, the force driving the universe toward greater disorder, ensures that all systems—though they may temporarily maintain order and resist decay—will eventually decline. Growth, adaptation, and the preservation of complexity come at a cost: they accelerate the entropic processes both inside the system and in its environment.

This principle applies to a wide range of everyday phenomena. Consider a business that starts small, grows, and thrives by attracting customers and adapting to market demands. Over time, the company requires more resources—capital, personnel, and innovation—to sustain its operations. As the business grows, it begins to encounter increasing costs and inefficiencies, which are the economic equivalent of accumulating entropy. External factors, such as competition or shifts in technology, further disrupt its internal balance. Eventually, without continued adaptation or an infusion of new resources, the business may stagnate or decline. Much like natural systems, businesses are subject to the pressures of entropy, where organizational complexity and growth eventually lead to inefficiencies and decline.

A similar dynamic occurs in the realm of technology. Consider the lifecycle of a popular consumer device, such as a smartphone. In its early years, it represents cutting-edge innovation, drawing on the latest technology to meet market demands. However, as newer models emerge, older devices begin to lose their competitive edge. Batteries degrade, software becomes outdated, and the cost of repairs starts to exceed the device’s value. This is a classic example of technological obsolescence, where entropy—in the form of wear and tear, technological advancement, and market shifts—drives the product toward eventual disuse and replacement.

The same principle can be seen in more abstract systems, such as financial markets. Market bubbles, for instance, experience rapid growth as investor confidence builds. Initially, the feedback loops of rising prices encourage further investment, driving expansion. However, as the system becomes increasingly strained—due to overvaluation, speculative behavior, or external economic shocks—the market’s internal entropy accumulates. Eventually, the bubble bursts, leading to a correction or collapse. This cycle of growth and decline is a direct manifestation of entropy at work within economic systems.

The decline of ecosystems and the collapse of civilizations offer even broader examples of entropy’s reach. Ecosystems grow and thrive by balancing resource availability and species interactions. However, over time, environmental changes, resource depletion, or human intervention may tip this balance, leading to a breakdown of the system. Similarly, historical civilizations, such as the Roman Empire, expanded and maintained vast networks of trade, culture, and political influence. Yet, over centuries, internal inefficiencies, resource exhaustion, and external pressures—entropic forces—led to their eventual decline.

In all these cases, whether in businesses, technology, markets, ecosystems, or civilizations, entropy drives the cycle of growth, adaptation, and eventual decline. Subsystems within the universe cannot maintain their internal order forever. As they grow and evolve, they consume resources and accelerate entropy, leading to a point where further growth becomes unsustainable. This is why, according to the laws of thermodynamics, all subsystems are inherently ephemeral: they must eventually succumb to the forces of entropy and decline.

The Ephemerality of Subsystems: Why Systems Must Eventually Die

Why must all subsystems eventually die? The answer lies in the fact that subsystems are open systems that rely on continuous energy exchanges with their surroundings. These exchanges sustain internal order, but they also accelerate entropy at the universal level. While subsystems may delay entropy for a time, their very existence contributes to the overall increase in entropy within the universe, which is the only truly closed system.

Peter Atkins’ analogy of entropy ratchets explains this well. Subsystems, like ratchets, can temporarily resist entropy by drawing on low-entropy resources from their environment. But over time, this process of maintaining order becomes unsustainable. As resources deplete or external disruptions occur, the internal structure of the system collapses under the weight of its own entropy. Growth, adaptation, and evolution are natural, but so too are decay and death.

In essence, subsystems are ephemeral because they exist within a closed universe governed by the second law of thermodynamics. The longer a system persists, the more energy it consumes and the closer it gets to its inevitable breakdown. Growth and evolution are temporary phases in a system’s life cycle, driven by the same forces that will ultimately cause its decline.

Entropy and Iteration: The Fuel for Systemic Evolution

We have emphasized the role of iteration in driving system evolution in previous posts, but now we see that entropy provides the fuel for these iterative processes. Entropy-driven energy exchanges propel systems to adapt, grow, and evolve. Whether it’s the interaction of organisms in an ecosystem or the rise and fall of stock prices in financial markets, each interaction expends energy, contributing to the overall entropy of the system.

At each iterative step, systems must adapt to new conditions, driven by the flow of energy from their environment. This energy exchange not only powers the system’s growth but also ensures that evolution remains time-asymmetric—that is, systems move forward in time as they adapt to entropy’s demands. Over time, however, the forces of entropy accumulate, and no system can maintain its internal order forever. This explains why life, death, growth, and decline are all essential parts of the natural cycle.

Entropy as the Dynamo of System Evolution: A Positive Force for Growth

While entropy is often associated with decay and disorder, it is crucial to recognize that it also plays a constructive role in driving growth, adaptation, and evolution. Systems don’t simply exist in a state of inevitable decline. Instead, they harness energy from their surroundings to sustain complexity for a time, delaying the effects of entropy. This process is what Erwin Schrödinger referred to as “negentropy” in his seminal work What is Life?—the idea that living systems temporarily reverse the trend toward disorder by importing low-entropy energy from their environments.

Negentropy is not just a biological concept; it applies to all complex adaptive systems. Every subsystem, whether a living organism, an ecosystem, or even a business or technology, relies on extracting energy or resources from its surroundings to maintain internal order. In this way, entropy serves as a positive force, powering the system’s capacity to grow, innovate, and adapt.

Consider how biological organisms sustain themselves. From the moment of birth, organisms tap into their environment—consuming food, sunlight, and oxygen—to fuel growth and maintain homeostasis. This continuous energy intake allows them to develop, adapt, and thrive, temporarily resisting the pull of entropy. Schrödinger described this as organisms “feeding on negative entropy,” a process that sustains life by reducing internal disorder even as the surrounding environment’s entropy increases. Plants, for example, convert sunlight into usable energy through photosynthesis, transforming low-entropy light into high-entropy waste products, while simultaneously maintaining internal order and structure.

This same principle applies to non-biological systems as well. For instance, a growing business or economy extracts resources from its environment—capital, labor, or raw materials—and converts them into products, services, and wealth. As long as the system can efficiently convert these resources into value, it sustains growth, delays decay, and temporarily pushes back the forces of entropy. New technologies and innovations emerge, markets expand, and new opportunities arise, all fueled by the energy and resources that the system continuously draws in.

Schrödinger’s concept of negentropy highlights the essential balancing act between order and disorder. Subsystems can grow and maintain complexity for a time by tapping into external resources, but they are always expelling entropy into their surroundings, contributing to the overall disorder of the universe. This gives rise to the cyclical nature of systems, where periods of growth, stability, and eventual decline are intertwined with the fundamental process of energy exchange and entropy management.

In technological systems, negentropy is evident in the evolution of AI and machine learning algorithms. These systems rely on massive amounts of data (a form of low-entropy input) to improve their capabilities. As more data is processed, AI systems learn and adapt, improving their accuracy and functionality. The process of feeding the system with new data allows it to resist the inevitable decline into obsolescence for a time. Yet, like all systems, AI models will eventually face limitations as their efficiency peaks, data becomes redundant, or newer technologies emerge, leading to their eventual decline.

In financial markets, negentropy operates through cycles of investment and innovation. A company may experience rapid growth by capitalizing on new technology, expanding its market share, and attracting investors. These inputs provide the energy needed to maintain the company’s competitive edge, allowing it to stave off entropy. However, as market conditions shift, resources become scarce, or the company faces disruption from competitors, it eventually reaches a point where sustaining growth is no longer possible. The forces of entropy, which had been delayed, begin to take hold, leading to a slowdown, restructuring, or even collapse.

The key takeaway here is that entropy is not purely a force of destruction. It is also the dynamo that powers the iterative processes of growth and adaptation in complex systems. As systems “feed” on negentropy, they temporarily maintain order and create complexity. This positive role of entropy ensures that systems evolve and adapt, taking advantage of the low-entropy resources available to them before succumbing to the eventual increase in disorder.

But this energy exchange is finite. The process of resisting entropy cannot last forever. As subsystems grow and evolve, they consume increasing amounts of energy, contributing to the total entropy of the universe—the only closed system. Over time, these subsystems reach a point where the energy required to maintain internal order exceeds what can be extracted from their environment. At this point, the forces of entropy take over, leading to the natural cycle of decline and dissolution.

In summary, entropy plays a dual role in complex systems: it drives growth and innovation by enabling systems to harness energy and resources from their environment, while also ensuring that no system can maintain its structure indefinitely. Schrödinger’s concept of negentropy captures this delicate balance, showing how systems can temporarily resist disorder and sustain complexity before ultimately succumbing to the inexorable increase in entropy. By understanding entropy as a positive force, we gain a more nuanced view of how systems evolve, adapt, and eventually decay, with growth and decline both emerging as natural outcomes of the same fundamental processes.