Based on the provided sources, trapped states in non-ergodic systems constitute the physical mechanism that preserves biological accidents, converting chance events into permanent, defining constraints of life (such as the genetic code).
Here is the detailed relationship between these concepts:
1. Non-Ergodicity and the “Freezing” of Phase Space
In a standard ergodic system (like a gas in a box), particles visit all possible microstates over time. Biological systems, however, are non-ergodic; the space of possible states is so vast that the system can only ever visit a tiny fraction of them[1].
• Broken Ergodicity: For a system to store information (memory) or maintain a structure, it must not be able to spontaneously transition between all states. As noted by Parrondo et al., reliable information storage requires that ergodicity be effectively broken, partitioning the phase space into distinct regions separated by high energy barriers[2][3].
• Trapped States: Because the system cannot explore the whole space, it gets “trapped” in specific regions (basins of attraction). In the context of self-organized criticality, systems may settle into a “frozen” or absorbing state where macroscopic evolution stops or becomes confined to a specific attractor[4][5].
2. The “Frozen Component” as a Biological Accident
Stuart Kauffman uses Random Boolean Networks to model how these trapped states relate to biological structure. When such a network operates above a certain connectivity threshold, a “frozen component” percolates across the system[6][7].
• Walls of Constancy: In this state, a large fraction of the variables (genes or chemical species) fall into fixed active or inactive states. These frozen components form “walls of constancy” that isolate other parts of the network[7].
• The Accident: Which specific variables freeze, and into what state (0 or 1), depends on the initial conditions and the specific “wiring” of the network. This is the accident. However, once the component freezes, that accident is locked in. The system effectively “boxes” itself into a tiny volume of its state space[8].
• Biological Correlate: Kauffman explicitly connects this to the differentiation of cell types. The “frozen core” corresponds to genes that are active (or inactive) in all cell types of an organism—a stable, historical accident of the genome’s architecture[9].
3. “Locked-In” Features and the Genetic Code
Peter Wills applies this logic to the origin of the genetic code, describing it as a “bootstrap” process of semantic inheritance.
• The Palimpsest: The specific assignment of codons to amino acids is an arbitrary “biological accident.” However, once the machinery (interpreters like Aminoacyl-tRNA synthetases) evolved to enforce these assignments, the system became trapped in that specific coding scheme[10].
• Locked-in Features: Wills argues that the coexistence of two distinct classes of these enzymes (Class I and II) is a “locked-in feature” left over from the invention of the code. In a purely competitive (ergodic/mixing) environment, one might have eliminated the other. But because the system is non-ergodic and relies on self-reference, these structures are trapped in a cooperative survival state[11].
4. Stability Allowing Evolution
Paradoxically, becoming “trapped” in a non-ergodic state is what allows biological evolution to proceed.
• Evolvability: If a system were fully ergodic (chaotic), a small perturbation would propagate damage everywhere, destroying information. “Trapped” or frozen states prevent damage from spreading, allowing “islands” of the system to adapt without destroying the whole[6][12].
• Memory: As noted by Vallino and Huber, abiotic systems maximize entropy production instantaneously, whereas biological systems use stored information (frozen history) to maximize entropy production over long time intervals[13][14]. The trapped state is the physical instantiation of this memory.
Summary: In a non-ergodic universe, a “biological accident” is a random configuration that the system falls into. The “trapped state” is the thermodynamic mechanism (energy barriers, frozen components) that prevents the system from leaving that configuration. This turns a momentary accident into a permanent constraint[15] that guides all future evolution.
References
[1] fourth law of thermodynamics.pdf [2] Nature Review - Thermodynamics of Information.pdf [3] Porrondo - Thermodynamics of Information.pdf [4] Demirel 2019 - Organised Structures Nonequilibrium Thermodynamics.pdf [5] Demirel 2019 - Organised Structures Nonequilibrium Thermodynamics.pdf [6] [Book] Zurek - Complexity, Entropy and the Physics of Information.pdf [7] [Book] Zurek - Complexity, Entropy and the Physics of Information.pdf [8] [Book] Zurek - Complexity, Entropy and the Physics of Information.pdf [9] [Book] Zurek - Complexity, Entropy and the Physics of Information.pdf [10] Wills Genetic Information Physical Interpreters and Thermodynamics the material information basis of biosemiosis.pdf [11] Wills Genetic Information Physical Interpreters and Thermodynamics the material information basis of biosemiosis.pdf [12] [Book] Zurek - Complexity, Entropy and the Physics of Information.pdf [13] Is the Meximum Entropy production just a heuristic principle - metaphysics on natural determination.pdf [14] [Book] Dewar - Beyond the Second Law Entropy Production and Non-equilibrium Systems.pdf [15] herrmann-pillath2011 - triadic conceptual structure on max entropy.pdf