| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Studies macroscopic behavior arising from ensembles of microscopic states; excludes single-particle or purely deterministic, non-probabilistic descriptions. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates between microscopic (molecular) and macroscopic (thermodynamic) levels, connecting particle dynamics to bulk observables. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | Microstates, particles, ensembles, phase-space points, energy levels, probability distributions, constraints. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Energy, momentum, configuration, degeneracy, probability weights, conserved quantities, statistical correlations. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Ensembles (microcanonical, canonical, grand canonical), states, phases, degrees of freedom, equilibrium vs nonequilibrium regimes. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Temperature, entropy, pressure, particle number, volume, distribution functions, partition function parameters. |
| | Parameterization | How variables encode and represent the system’s state. | States encoded via probability distributions, partition functions, density operators, and collective order parameters. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Ideal gases, large-N limits, ergodicity, indistinguishability, weak interactions, continuum approximations. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Hold for sufficiently large ensembles, weak coupling, long timescales, or equilibrium conditions; break down for small systems or strong correlations. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Assumes randomness, ergodicity, energy conservation, ensemble equivalence under suitable limits, and probabilistic descriptions of microstates. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes time averages approximate ensemble averages, coarse-graining is meaningful, and microscopic laws underpin macroscopic regularities. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Requires that probability rules, microstate counting, and macroscopic thermodynamic relations not contradict one another. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Demands alignment between microscopic dynamics, ensemble definitions, conservation laws, and emergent thermodynamic equations. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | Fluctuations, probability distributions, heat flow, pressure, volume changes, correlations, phase transitions, relaxation behaviors. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Constrained by spatial resolution, temporal resolution, sensitivity to small fluctuations, and ability to resolve microscopic vs. coarse-grained dynamics. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Kelvin, joules, pascals, volumes, particle numbers, correlation lengths, relaxation times, entropy and information measures. |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Calorimeters, pressure sensors, neutron scattering instruments, NMR, optical probes, molecular simulation tools, large-scale statistical datasets. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Temperature defined via energy distribution; entropy via state counting; pressure via momentum transfer; correlations via measurable statistical averages. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Repeated sampling, time averaging, ensemble averaging, controlled perturbations, reproducible simulation protocols. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Collecting large datasets of fluctuations, repeated measurements for averaging, controlled initialization for relaxation studies, equilibrium and nonequilibrium runs. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Ensemble sampling, Monte Carlo sampling, time-series sampling, spatial grid sampling, representative subsets of microstates. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Time series, histograms, correlation functions, phase diagrams, probability distributions, simulation trajectories, macroscopic variable readings. |
| | Resolution | The granularity or precision with which data is captured. | Determined by sampling frequency, measurement granularity, number of microstates sampled, detector sensitivity, numerical precision. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Verifying temperature scales, pressure baselines, simulation time-step accuracy, statistical convergence, ergodicity checks. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Quantifying thermal noise, sampling error, finite-size effects, numerical errors, bias from insufficient equilibration or poor ensemble selection. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Boltzmann distribution, fluctuation–dissipation relations, equipartition theorem, equation of state relations, scaling laws near critical points. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Conserved quantities (energy, momentum, particle number), symmetry invariants, ensemble invariants, invariance of macroscopic relations under microstate exchange. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Microscopic interactions generating macroscopic observables; ergodicity; collision dynamics; relaxation toward equilibrium; correlated fluctuations. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Thermalization pathways, diffusion sequences, relaxation trajectories, phase-transition routes through configuration space. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Microstate, macrostate, ensemble, partition function, entropy, fluctuations, correlation length, order parameter. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Ensembles (microcanonical, canonical, grand canonical), phases, universality classes, equilibrium vs. nonequilibrium systems. |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Boltzmann equation, Liouville equation, partition function formulas, fluctuation–dissipation equations, Fokker–Planck dynamics. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Ising model, ideal gas models, lattice models, mean-field models, stochastic processes, Markov chains, molecular simulation frameworks. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Ideal gases, independent-particle models, mean-field approximations, coarse-grained lattices, continuum approximations. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Large-N limits, weak-coupling limits, near-equilibrium regimes, critical scaling limits, breakdown at small system sizes or strong correlations. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Connection between microscopic dynamics and thermodynamics; universality theory; renormalization-group frameworks. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Links to condensed matter physics, information theory, complex systems, chemical kinetics, stochastic processes, and materials science. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Manipulating temperature, volume, boundary conditions, or interaction strength to probe ensemble behavior and fluctuation properties. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Recording spontaneous fluctuations, correlation decay, transport properties, and equilibrium distributions without controlled perturbation. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Comparing predicted distributions, correlations, or relaxation laws with empirical data or high-fidelity simulations. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Reproducing measured distributions, critical exponents, relaxation curves, and simulation outcomes across different runs, instruments, or initializations. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Estimating parameters from noisy fluctuations, extracting critical behavior, fitting distribution forms, quantifying correlation lengths. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Evaluating lattice models, mean-field models, Monte Carlo predictions, or analytic approximations on accuracy, robustness, and scalability. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Quantifying finite-size effects, sampling error, numerical integration error, equilibration error, and detector noise. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Ensuring adequate sampling, avoiding biased initialization, verifying ergodicity, randomizing initial states, reducing algorithm-induced bias in simulations. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Independent review of ensemble choices, sampling methods, correlation analyses, and numerical techniques. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Updating models, approximations, scaling assumptions, or ensemble frameworks in response to discrepancies with experimental or computational data. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Disclosing sampling strategies, simulation parameters, equilibration times, statistical thresholds, analytical assumptions, and data-processing methods. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Maintaining honest reporting of statistical uncertainty, avoiding data manipulation, ensuring reproducibility, and responsibly handling large dataset analyses. |