Dynamical theory of complex systems with two-way micro–macro causation
Bibliographic record
Abstract
In many complex systems encountered in the natural and social sciences, mechanisms governing system dynamics at a microscale depend upon the values of state variables characterizing the system at coarse-grained, macroscale (Goldenfeld and Woese, 2011, Noble et al., 2019, and Chater and Loewenstein, 2023). State variables, in turn, are averages over relevant probability distributions of the microscale variables. Neither inferential Top–Down nor mechanistic Bottom–Up modeling alone can predict responses of such scale-entwined systems to perturbations. We describe and explore the properties of a dynamic theory that combines Top–Down information-theoretic inference with Bottom–Up , state-variable-dependent mechanisms. The theory predicts the functional form of nonstationary probability distributions over microvariables and relates the trajectories of time-evolving macrovariables to the form of those distributions. Analytic expressions for the time evolution of Lagrange multipliers from Maxent solutions allow for rapid calculation of the time trajectories of state variables even in high dimensional systems. Examples of possible applications to scale-entwined systems in nonequilibrium chemical thermodynamics, epidemiology, economics, and ecology exemplify the potential multidisciplinary scope of the theory. A worked-out low-dimension example illustrates the structure of the theory and demonstrates how scale entwinement can result in slowed recovery from perturbations, reddened time series spectra in response to white-noise input, and hysteresis upon parameter displacement and subsequent restoration.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".