Based on the provided sources, non-ergodicity fundamentally alters the predictability of evolutionary paths by shifting systems from a regime of statistical inevitability (where all states are eventually visited) to one of historical contingency, path dependence, and computational irreducibility.
In a non-ergodic evolutionary context, the space of possible states grows faster than the system can explore them, meaning the system never visits the same state twice and its future trajectory is determined by “frozen” accidents of the past rather than universal equilibrium laws.
1. The Expanding Phase Space and Zero Probability of Return
In standard statistical mechanics, an ergodic system eventually visits all compatible microstates, allowing observers to predict behavior based on ensemble averages. In evolutionary systems, this assumption fails because the state space is non-ergodic.
• Explosion of Possibilities: Herrmann-Pillath argues that in evolutionary systems, the space of possible states (combinations and partitions of components) increases much faster than the number of realized states. Consequently, the system traces a unique trajectory where the probability of returning to a previous state is arbitrarily close to zero[1].
• Radical Unpredictability: Because the system cannot explore the vast majority of the “adjacent possible,” the specific path taken is not determined by a global maximization of entropy across all possibilities, but by the specific, singular history of interactions. This creates a “horizon of indeterminacy” where future states cannot be algorithmically deduced from current conditions[2][3].
2. Path Dependence and “Frozen” Components
Non-ergodicity manifests in the “freezing” of specific configurations. Once a system settles into a specific functional basin, it is trapped there, and this historical choice constrains all future evolution.
• Frozen Components: Kauffman describes how complex networks develop “frozen components”—clusters of variables that fall into fixed states. These frozen cores percolate through the system, creating walls of constancy that functionally isolate other parts of the system[4][5].
• Effective Ergodicity Breaking: This partitioning of phase space into regions where the system remains for very long times is termed “effective ergodicity breaking”[6].
• Constraint on Adaptation: Because the system is trapped in these local regions (or “frozen accidents” like the specific genetic code), it cannot easily jump to potentially optimal states elsewhere in the fitness landscape. Evolution becomes a search constrained by where the system has been, rather than a global optimization of where it could be[7][8].
3. Temporal Strategies vs. Instantaneous Prediction
In abiotic (ergodic) systems, predictability is often based on the instantaneous maximization of entropy production (steepest descent). Non-ergodic biological systems break this rule by using stored information to predict and navigate the future.
• Temporal Strategies: Vallino and Huber argue that biotic systems differ from abiotic ones because they possess a genome (a record of successful past non-ergodic pathways). This allows them to implement “temporal strategies”—forgoing the immediate steepest descent of energy dissipation to follow pathways that yield greater returns over longer time intervals[9][10].
• Failure of Standard Models: Consequently, models that assume instantaneous maximization of entropy production (MaxEP) fail to predict biological behaviors because living systems use information to avoid the direct path to equilibrium[11].
4. Computational Irreducibility and the “Bootstrap”
The predictability of evolutionary paths is further limited because the “laws” governing the system are generated by the system itself during the process.
• Internal Causation: In the Earth system and biological evolution, there is no clear separation between the “hardware” (laws/constraints) and the “software” (dynamics). The system fabricates its own constraints through closure to efficient causation[2].
• Non-Computability: Because the specific functions and codings (like the folding of proteins) arise from self-referential causal loops, the specific phenotype cannot be computed or simulated purely from the genotypic information[2]. The evolution of such systems is “beyond physics” in the sense that there are no entailing laws that pre-state the functions that will emerge; a screwdriver can be used to turn a screw or crack a coconut, and which function evolves is a matter of historical bricolage, not deduction[12][13].
Summary
Non-ergodicity impacts predictability by ensuring that history matters. An evolutionary path is not a fluctuation around a mean (as in equilibrium thermodynamics) but a unique, irreversible trajectory where:
1. Global equilibrium is irrelevant because the system cannot explore the full state space[1].
2. Past accidents become future constraints (frozen components)[4].
3. Prediction requires knowledge of the specific information content (genome/memory) the system uses to navigate, rather than just external physical forces[10].
References
[1] fourth law of thermodynamics.pdf [2] entropy-23-00915.pdf [3] entropy-23-00915.pdf [4] [Book] Zurek - Complexity, Entropy and the Physics of Information.pdf [5] [Book] Zurek - Complexity, Entropy and the Physics of Information.pdf [6] Porrondo - Thermodynamics 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] Dewar - Beyond the Second Law Entropy Production and Non-equilibrium Systems.pdf [10] [Book] Dewar - Beyond the Second Law Entropy Production and Non-equilibrium Systems.pdf [11] [Book] Dewar - Beyond the Second Law Entropy Production and Non-equilibrium Systems.pdf [12] entropy-22-01163.pdf [13] entropy-22-01163.pdf