Information, order, complexity, and entropy in materials including biological systems: a thermodynamic theory based on state variables
This paper proposes a unified thermodynamic theory that resolves ambiguities regarding entropy, information, and complexity in materials and biological systems by redefining state variables as time-averaged atomic positions, thereby distinguishing entropy as uncertainty in these variables rather than information itself while preserving the third law.
Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Entropy is a word that often appears in discussions about the universe's tendency toward chaos, but in the scientific study of materials, it is a precise measurement of a system's state. For over a century, physicists have used thermodynamics to describe how energy moves and how systems settle into balance. A central pillar of this field is the idea that entropy is a state function, meaning its value depends only on the current condition of the material, not on how it got there. This concept works beautifully for gases, where the behavior of the whole is determined simply by temperature and volume. However, when scientists try to apply these same rules to solids, especially complex ones like glass or the DNA inside living cells, the definitions begin to blur. A major point of confusion has been whether the "disorder" of a material's internal structure counts as entropy, or if that disorder is actually a form of information. This ambiguity has led to contradictions, such as the suggestion that some materials might retain a hidden amount of entropy even at absolute zero, which would break a fundamental law of physics known as the third law.
A researcher named Koun Shirai has proposed a new way to resolve these contradictions by returning to the strict definitions of thermodynamics and applying them to the microscopic world of atoms. The core of the work involves redefining what it means for a solid to be in equilibrium. Traditionally, scientists assumed that for any given temperature and volume, a solid could only exist in one perfect, defect-free state. Shirai argues that this view is incomplete. Instead, he suggests that the true state of a solid is defined by the specific, time-averaged positions of every single atom within it. Because atoms in a solid vibrate around fixed points, these average positions act as the material's unique coordinates. This perspective reveals that a solid can exist in many different equilibrium states simultaneously, even at the same temperature, depending on where its atoms happen to be settled.
By establishing that these atomic positions are the fundamental variables that define a material's state, the paper clarifies the relationship between entropy, order, and information. The author concludes that entropy is not a measure of the information stored in a material, nor is it a measure of disorder. Rather, entropy measures the uncertainty or thermal fluctuations associated with those specific atomic positions. The information itself—the unique structure that makes a piece of glass different from a crystal, or a specific DNA sequence different from another—is carried by the positions of the atoms themselves. This distinction allows scientists to separate the concept of "order" from simple geometric patterns. A material can be highly ordered and carry vast amounts of information even if it lacks a repeating, crystal-like pattern, as long as its atomic positions remain stable over time.
This framework also solves the long-standing puzzle of "residual entropy," the idea that some materials seem to keep a bit of entropy even when cooled to absolute zero. The paper explains that this apparent leftover entropy is actually an artifact of how we measure it. When a material like glass cools down, the atoms get locked into a specific arrangement that they cannot easily change. In thermodynamic terms, the variables that described the many possible arrangements at higher temperatures become "frozen." They no longer fluctuate, so they stop contributing to the current entropy of the system. The value we calculate as residual entropy is actually a memory of the many states the material could have been in before it froze, not a property of the state it is in now. When the entropy is calculated correctly based only on the active, fluctuating variables of the current state, it correctly drops to zero at absolute zero, preserving the third law of thermodynamics.
The implications of this work extend to how we understand complexity and information processing in both machines and living things. If information is defined by the number of stable atomic arrangements a material can hold, then even a simple crystal is incredibly complex because it contains billions of atoms, each with its own position. This explains how a silicon chip can store massive amounts of data; it does so by switching between different stable arrangements of defects within the crystal, not by being a random mess. Similarly, in biology, the diversity of life forms arising from a single genetic code can be understood as the system moving between different stable equilibrium states. The paper suggests that biological evolution and information processing are not violations of thermodynamic laws but are processes of navigating between these stable states, driven by energy flows that allow the system to overcome the barriers separating them. By grounding these concepts in the precise behavior of atoms, the study offers a unified view where the laws of physics apply consistently from the smallest crystal to the most complex living organism.
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