First Principles Framework (FPF)

• FPF is a systematic modeling approach that derives equations from fundamental laws, ensuring accuracy and minimal empirical assumptions.
• It spans diverse domains such as quantum theory, materials science, and AI risk, rigorously applying microphysical and mathematical principles.
• FPFs enable computational automation and upscaling, delivering quantitative predictions with clear, systematically improvable approximations.

A First Principles Framework (FPF) is a modeling or computational strategy in which all relevant physical, chemical, informational, or socio-technical processes are derived strictly from underlying laws or mechanistic axioms, rather than constructed from empirical fitting or ad hoc assumptions. FPFs have been formulated in domains as varied as condensed matter physics, quantum theory, population dynamics, phase-field modeling, risk assessment, and plasma turbulence. This article surveys the general architecture, operational principles, and prototypical realizations of First Principles Frameworks across multiple research domains.

1. Core Concepts and Architectural Principles

The distinguishing hallmark of a First Principles Framework is the explicit and systematic derivation of equations, models, or workflows from the foundational laws of the relevant microphysics or mathematical logic. In computational materials science, this typically means direct use of quantum mechanics via density functional theory (DFT), many-body perturbation theory, or their extensions; in information theory or AI governance, it manifests as risk analysis stratified by ontological categories of information and their semantic consequences.

FPFs generally comprise the following elements:

• Primitive physical or information-theoretic laws: Such as the Kohn–Sham equations, the Liouville–von Neumann equation, or axioms of convex operational frameworks.
• Systematic upscaling and coarse-graining: For phase-field models or population biology, the transition from microscale (atomistic, agent-based) dynamics to mesoscale or continuum descriptions is performed through established mathematical limits or Bayesian probabilistic inference.
• Self-consistent coupling: All interactions, boundary conditions, and couplings (e.g., electron–phonon, spin–orbit, stochastic transitions) are incorporated at the correct level, propagating the influence of microphysical effects upwards without phenomenological fitting.

This systematic, reductionist approach enables the direct prediction of observables (e.g., mobility, relaxation rates, or emergent societal risks) with minimal or no reliance on experimental calibration, with all approximations and closures explicitly stated and, in many cases, systematically improvable.

2. Exemplary Mathematical Formalisms and Key Equations

The mathematical apparatus of each FPF is determined by the target domain but always exhibits derivation from explicit microphysical principles. Representative structures include:

• DFT + DFPT + Boltzmann Transport (2D Mobility):

$$g_{mn,\nu}(k,q) = \sum_{a,i} e_{q,\nu}^{a,i} \sqrt{\frac{\hbar}{2M_a \omega_{q,\nu}}} \langle \psi_{m,k+q} | \frac{\partial V_{KS}}{\partial u_{a,i}(q)} | \psi_{n,k} \rangle$$

which feeds into

$$P_{nk \rightarrow m k+q}^{\nu} = \frac{2\pi}{\hbar} \frac{1}{N_q} |g_{mn,\nu}(k,q)|^2 \{ n_{q,\nu}\delta(\epsilon_{m,k+q} - \epsilon_{n,k} - \hbar\omega_{q,\nu}) + ...\}$$

assembled into an iterative solution of the linearized BTE beyond the relaxation time approximation (Sohier et al., 2018).

• Quantum Theory from Positive Formalism:

$$(b, c) = \text{Tr}(b\,c), \quad Q(\rho) = \sum_i K_i \rho K_i^\dagger$$

$p(k|\psi) = |\langle \eta_k | \psi \rangle|^2$

$i\hbar \frac{d}{dt} |\psi\rangle = H |\psi\rangle$

derived by a stepwise imposition of partial order, composition, spacetime locality, and causality (Oeckl, 2019).

• Population Dynamics Master Equation:

$$\frac{d}{dt} \Pi_{\mathbf{n}}(t) = \sum_{r=1}^R [W_r(\mathbf{n}-\mathbf{S}_r)\,\Pi_{\mathbf{n}-\mathbf{S}_r}(t) - W_r(\mathbf{n})\,\Pi_{\mathbf{n}}(t)]$$

with

$$W_r(\mathbf{n}) = k_r \prod_i \frac{n_i!}{(n_i - s_{ir})! s_{ir}! \Omega^{s_{ir} - 1}}$$

leading to deterministic ODEs in the large system-size limit (Araujo, 2023).

• Information-Risk Category Classifier:

$$f : \mathcal{I} \longrightarrow \mathcal{C}, \quad f(i) = \begin{cases} 1 & \text{perceptual signal} \ 2 & \text{propositional knowledge} \ 3 & \text{decision/action plan} \ 4 & \text{control token} \end{cases}$$

together with

$$R_{\text{out}^{(k)}} = P_{\text{fail}^{(k)}} \times S^{(k)}$$

for outcome risk assessment (Tong et al., 31 Mar 2025).

3. Domain-Specific Implementations and Workflows

3.1 Electronic and Phononic dynamics

The FPF for 2D materials (Sohier et al., 2018), and the broader framework covering electron–phonon interactions (Bernardi, 2016), build mobility and scattering calculations without empirical parameters. The workflow proceeds:

• DFT for ground-state structure and density.
• DFPT for phonons and electron–phonon matrix elements, accounting for real dopant density and 2D Coulomb truncation.
• Symmetry-enabled identification of irreducible k- and q-points.
• Construction and interpolation of e–ph matrix elements.
• Solution of the linearized BTE beyond RTA, iteratively accounting for scattering-in terms.

This yields predictions such as room-temperature mobility values (e.g., hole-doped phosphorene, 586 cm²/Vs), quantitative temperature dependence (μ ~ T^–γ, γ ≈ 1–1.5), and clarifies the limiting role of intervalley scattering and valley anisotropy.

3.2 Spin Transport and Defect Dynamics

FPFs for spatio-temporal spin transport (Fadel et al., 12 May 2025) and spin-defect intersystem crossing (Jin et al., 27 Feb 2025) advance from quantum density-matrix dynamics (Liouville–von Neumann, Wigner formalism) and many-body correlated active space electronic structure. This enables:

• Direct simulation of coherent and incoherent (scattering-limited) spin propagation, correctly recovering the free-induction decay, Dyakonov–Perel, and Elliott–Yafet regimes as emergent limits.
• Computation of quantum-defect transition and relaxation rates with ab initio SOC and vibronic couplings, systematically eliminating cluster-size artifacts through finite-size extrapolation.

3.3 Glassy and Nonequilibrium Dynamics

The FPF of Janssen and Reichman for supercooled liquids (Janssen et al., 2015) constructs a hierarchy of kinetic equations based only on the static two-point structure factor S(k), retaining high-order dynamical correlations and systematically improving over standard MCT closures.

3.4 Information Classification and Risk

The IEEE P3396-aligned FPF (Tong et al., 31 Mar 2025) classifies all AI-generated artifacts by their semantic type, enabling risk quantification and stakeholder responsibility mapping across the perception, knowledge, decision/action, and control-token layers. This harmonizes risk assessment across modalities and supports precise assignment of mitigations.

4. Computational Strategies and Automation

High-throughput adoption of FPFs typically requires robust algorithmic workflows:

• Irreducible domain and symmetry reduction: Use of crystal group operations and energy-based pocket selection to reduce BZ sampling effort (Sohier et al., 2018).
• Iterative solution of coupled kinetic equations: For both transport (BTE) and dynamical density correlation hierarchies.
• Spline-based variational force matching: To parametrize coarse-grained free energy terms in phase-field upscaling (Jin et al., 2024).
• Explicit boundary conditions and mesh management: Essential in transport, trajectory sampling, and non-equilibrium phenomena.
• Parallelization and basis interpolation: Leverage Wannier functions, FFT grids, and symmetry to enable fine-mesh calculations necessary for converged transport or lifetimes (Bernardi, 2016).

5. Validation, Scope, and Systematic Corrections

The predictive reliability of an FPF is evaluated through systematic convergence (e.g., closure order in MCT-like hierarchies), comparison with simulation and experiment, and parametric/numerical robustness tests (e.g., kernel regression in EMS spatial decay (Kikuchi, 23 Oct 2025)). Open questions typically center on:

• Corrections from higher-order couplings or non-Markovian effects.
• Inclusion of electronic correlation, strong coupling, or long-range structural information (e.g., multi-point structure factors).
• Scalability to complex heterogeneous systems, such as polydisperse glasses or real-time ARPES under pump–probe.

FPFs maintain extensibility by structuring all model components (dynamics, couplings, closures) in a modular, interoperable fashion. This uniformity supports swapping or refining modules (e.g., to incorporate electron–electron scattering or multiphase coarse-graining).

6. Tables: Cross-Domain Exemplars and Their Core Principles

Domain	Core FPF Elements	Reference
2D carrier transport	DFT + DFPT + on-the-fly EPC + iterated BTE	(Sohier et al., 2018)
Quantum theory	Positive cone, operational composition, anti-lattice logic	(Oeckl, 2019)
Population/ecological dynamics	Master equation, explicit counting, Bayesian inference	(Araujo, 2023)
Information risk (AI governance)	Information-centric, semantic category, formal risk map	(Tong et al., 31 Mar 2025)
Phase-field modeling	Atomistic–CG–field upscaling, force-matching, variational	(Jin et al., 2024)
Glass/electrolyte dynamics	S(k)-only kinetic hierarchy, closure-systematic	(Janssen et al., 2015)
Spin transport in crystals	Real-time density matrix + Wigner drift	(Fadel et al., 12 May 2025)
Shear suppression of plasma turbulence	Non-asymptotic analytic decorrelation, cubic root law	(Hatch et al., 2017)

Each implementation retains strict traceability to first-principles laws and a workflow enabling refinement, upscaling, and quantitative prediction in the target domain.

7. Impact, Limitations, and Outlook

First Principles Frameworks offer domain-independent strategies for high-accuracy, mechanistically transparent prediction. Their distinctives are:

• Predictivity and minimal empiricism: Theoretical predictions agree closely with experiment or simulation over broad windows without intermediate fitting.
• Clarity of approximations and boundaries: All closures, upscaling steps, and simplifications are parameterized and, in many cases, improve systematically.
• Algorithmic automation potential: FPFs can be translated into end-to-end protocols ranging from automated DFT-transport pipelines to modular Bayesian/Ecological inference environments.

Limitations include the computational cost (especially for high-fidelity many-body calculations), current constraints on including all relevant many-body or non-perturbative effects, and the potential need for domain-specific closure rules whose first-principles justification may itself be challenging.

Nonetheless, as computational power and methodological advances continue, FPFs serve as the structural backbone for quantitative mechanistic science in both physical and information domains. Their modularity and theoretical rigor are likely to dominate future efforts in ab initio modeling, multiscale simulation, and principled risk assessment.