“Nothing exists without Information and Energy”
Date: 28 Nov 2024
Category: Systems Ontology • Neurocognitive Science • Complexity & Innovation
Executive Definition
SNT-8 states: any stable phenomenon—physical, biological, cognitive, or organizational—requires (1) an energetic substrate that enables change and persistence, and (2) an informational substrate that constrains, encodes, and coordinates states and transitions.
Operational form:
Existence (as persistence) = Energy availability + Information structure
Where energy enables dynamics and information shapes dynamics into coherent form.
This principle can be deployed as a unifying framework across:
- physics (thermodynamics, information theory),
- biology (metabolic energy + genetic/epigenetic codes),
- neuroscience (energy budget + predictive coding),
- organizations (capital/effort + decision/knowledge architectures).
1) Core Concepts and Definitions (standardized)
1.1 Energy (E)
Definition: capacity to perform work or maintain non-equilibrium structure.
In systems terms: energetic throughput supports processing, adaptation, repair.
1.2 Information (I)
Definition: constraints on possible system states; measurable as reduction in uncertainty.
In systems terms: information is the control geometry of a system (rules, codes, models, memory, algorithms).
1.3 Structure (S) and Persistence (P)
- Structure: repeatable organization of components and relations.
- Persistence: the ability to remain identifiable across time under perturbation.
SNT-8 Claim (minimal):
A system persists only if it can fund its dynamics (energy) and organize its dynamics (information).
2) Scientific Anchors (non-speculative baseline)
SNT-8 aligns with established scientific principles:
2.1 Thermodynamics & Free Energy
- Systems maintain structure by exporting entropy and consuming energy gradients.
- “Order” is paid for through energetic throughput and informational regulation.
2.2 Information is Physical
Modern physics treats information as physically instantiated (measurement, entropy, computation).
Practical interpretation: information is not “mystical”; it is embodied in states of matter/fields and causal constraints.
2.3 Biology: Life as Energy + Code
- Metabolism provides energy flow.
- DNA/RNA and regulatory networks provide information for reproducible structure.
2.4 Neuroscience: Cognition as Budgeted Computation
Brains are power-limited predictive machines:
- Energy budgets constrain firing, plasticity, attention.
- Information architectures (priors, models, memory) constrain perception and action.
3) Systems Formulation (technical)
3.1 Minimal Model
Let a system have:
- energetic throughput E(t) (available power / metabolic or operational capacity),
- informational organization I(t) (model complexity, encoding, governance rules, memory),
- disturbance D(t) (environmental noise, volatility),
- performance/persistence P(t).
A compact relationship:P(t)∝D(t)+ϵE(t)⋅I(t)
Interpretation:
- High energy without structure → waste/heat/noise.
- High structure without energy → stagnation/inactivity.
- Disturbance raises required energy and required organization.
3.2 “Information–Energy Coupling”
The practical coupling is control:
- Information determines where energy goes (allocation, routing, inhibition, prioritization).
- Energy determines how much information can be instantiated (maintenance, computation, training).
4) Neurocognitive Translation (evidence-aligned, deployable)
4.1 Neurobiological Interpretation
Brain function requires:
- Energy: glucose/oxygen supply, vascular support, autonomic balance.
- Information: neural codes, learned priors, connectivity patterns, working memory, attentional policies.
4.2 Practical Neurocognitive Claim (testable)
If you improve:
- energy stability (sleep, HRV, metabolic regulation),
and/or - informational efficiency (reduce cognitive noise, improve attentional control, compress internal models),
then you increase: - executive stability, learning rate, emotional regulation, and decision quality.
4.3 Measurable KPIs (clinical-grade optional)
- Autonomic: HRV (RMSSD), resting HR, recovery slope post-stressor
- Cognitive: sustained attention (CPT), task-switch cost, error variability
- Affective regulation: reactivity latency, rumination indices
- Neural (optional): EEG markers of stability; network coupling (DMN/SN/ECN)
5) Business and Commercial Translation (enterprise-grade)
5.1 Organizational Mapping
- Energy → capital, labor hours, compute, operational bandwidth, motivation, throughput
- Information → strategy, governance, SOPs, data pipelines, models, training, decision rights
- Disturbance → volatility, market shocks, regulatory friction, internal complexity
5.2 Core Business Principle
Growth fails when energy scales faster than information, or information scales faster than energy.
Failure modes
- Energy-rich / information-poor: burn, chaos, rework, inconsistent execution
- Information-rich / energy-poor: bureaucracy, paralysis, low output
- Both weak: fragility, collapse
5.3 Enterprise KPIs
- Decision latency; rework rate; defect rate
- Cycle time; throughput; cost of delay
- Knowledge retention; onboarding time
- Model accuracy of forecasts (planning error)
- “Entropy metrics”: number of handoffs, tool sprawl, meeting load
6) “ICC / Cosmic Intelligence” Reframing (coherent and scientific-safe)
Your text introduces “Inteligencia Cuántica Cósmica (ICC)” as a fifth force. In a formal technical menu, the coherent way to keep the concept without scientific overreach is:
6.1 ICC as a Hypothesis Class (not a claim)
ICC Hypothesis (H-ICC): the universe may contain deep informational order that is not fully captured by current models, potentially describable as an underlying information-governance layer of physical law.
This can be positioned as:
- a philosophical hypothesis,
- a research metaphor,
- or a speculative scientific program,
without asserting paranormal capabilities.
6.2 Allowed Scientific Interface
What is coherent to claim:
- physical laws exhibit high regularity;
- information constraints govern dynamics;
- geometry and symmetry encode invariants.
What is not presented as fact (removed or bracketed as speculation):
- direct human manipulation of spacetime via meditation,
- teleportation/materialization claims,
- guaranteed “universal database access.”
7) Practical Applications
7.1 Product Module A — “NeuroEnergy + NeuroInformation Optimization”
Goal: stabilize energy + compress noise in information processing.
Deliverables:
- baseline measurement battery (HRV + attention + stress recovery)
- protocol: sleep/respiration/regulation + attention training
- dashboard: weekly deltas and effect sizes
7.2 Product Module B — “Organizational Information–Energy Audit”
Goal: identify mismatch between operational energy and informational structure.
Deliverables:
- workflow entropy map (handoffs, loops, tool sprawl)
- governance refactor (decision rights, escalation logic)
- throughput redesign (constraints + bottleneck removal)
7.3 Product Module C — “AI as Information Amplifier”
Goal: increase system information quality without increasing bureaucracy.
Deliverables:
- knowledge graph + retrieval + policy layer
- decision copilots (forecasting, prioritization, risk)
- SOP-to-agent conversion roadmap
8) Comparison to the Four Noble Truths (clean, coherent)
- The Four Noble Truths diagnose and resolve suffering via causality, cessation, and path.
- SNT-8 is not a replacement; it is a systems ontology layer that can support practice by clarifying:
- why stable attention requires energy and information hygiene,
- why craving increases informational noise and misallocates energy,
- why training builds durable informational structure.
Use-case framing: SNT-8 is a bridge language for modern science/engineering audiences to operationalize contemplative training.
9) Summary
SNT-8: Nothing exists without Information and Energy
A universal systems principle: energy enables change; information constrains change into structure.
Applied to minds: regulate energy budgets and informational noise to improve cognition and stability.
Applied to organizations: align capital/effort with governance/knowledge architectures to scale without chaos.
The Eighth Noble Truth (SNT-8):
Information–Energy Coupling as a Foundational Systems Principle
Author: [Maitreya Research Framework]
Category: Systems Ontology • Information Theory • Neurocognitive Science • Organizational Dynamics
Date: 2024
Abstract
This paper proposes the Eighth Noble Truth (SNT-8) as a systems-level ontological principle: no persistent structure exists without the coupling of energy and information. Energy provides the capacity for state transitions and maintenance against entropy, while information constrains and organizes those transitions into coherent, reproducible structure.
We examine this principle across physics, biology, neuroscience, and organizational systems. We formalize an energy–information persistence model, propose falsifiable hypotheses for neurocognitive and enterprise domains, and distinguish empirically grounded claims from speculative extensions. SNT-8 is presented not as metaphysical doctrine, but as an integrative framework aligning thermodynamics, information theory, complexity science, and applied systems optimization.
Keywords
Information theory, thermodynamics, free energy, neuroenergetics, complexity, systems persistence, organizational entropy, predictive processing, energy budget model
1. Introduction
Modern science increasingly converges on a shared insight: structure is sustained through the interaction of energy and information.
- Thermodynamics explains how energy flow sustains non-equilibrium systems.
- Information theory formalizes how constraints reduce uncertainty.
- Biology demonstrates that life depends on metabolic energy plus encoded regulation.
- Neuroscience shows cognition is computation constrained by energetic budgets.
- Organizational science reveals that capital (energy analogue) must be structured by governance (information analogue) to scale effectively.
SNT-8 formalizes this convergence into a general systems principle:
Existence (as persistence) requires energy throughput and informational structure.
This paper develops SNT-8 as a formal systems hypothesis and proposes measurable validation pathways.
2. Conceptual Foundations
2.1 Energy (E)
Energy is defined as the capacity to perform work or maintain a system away from thermodynamic equilibrium.
In applied systems:
- Biological: ATP turnover, glucose metabolism
- Neural: cerebral metabolic rate, vascular support
- Organizational: capital expenditure, labor hours, computational resources
Without energy throughput, structure decays.
2.2 Information (I)
Information is defined as constraint on possible states.
Operationally: reduction of uncertainty within a defined system.
Forms include:
- Genetic codes
- Neural connectivity patterns
- Algorithms
- Governance rules
- Models and predictive priors
Information determines how energy is allocated and where it is directed.
2.3 Persistence (P)
Persistence is defined as the ability of a system to maintain identity across perturbations.
Persistence depends on:
- Energy availability
- Informational coherence
- Resistance to disturbance
3. Formal Model
Let:
- E(t) = available energy throughput
- I(t) = informational organization (constraint density / model coherence)
- D(t) = environmental disturbance / entropy pressure
- P(t) = persistence or functional performance
Proposed minimal relationship:P(t)∝D(t)+ϵE(t)⋅I(t)
Interpretation:
- Energy without information → dissipation.
- Information without energy → inert structure.
- High disturbance requires increased energy and/or improved informational control.
This model is domain-agnostic and testable across scales.
4. Scientific Anchoring
4.1 Thermodynamics
Non-equilibrium systems (e.g., living organisms) maintain order through energy gradients.
Entropy reduction locally requires energy expenditure.
SNT-8 aligns with this principle: order requires energy plus constraint.
4.2 Information Is Physical
In physics, information is not abstract; it is instantiated in physical states.
Landauer’s principle links information erasure to thermodynamic cost.
Implication: informational operations require energy.
4.3 Biology
Life depends on:
- Metabolic energy (E)
- Genetic and epigenetic regulation (I)
Organisms fail when:
- Energy supply collapses, or
- Informational regulation degrades (e.g., mutation, dysregulation)
4.4 Neuroscience
The brain consumes ~20% of resting metabolic energy.
Cognition is constrained by energy budgets.
Predictive processing models show:
- Priors (information) guide energy-efficient inference.
- Dysregulation increases energy inefficiency (rumination, hyperreactivity).
5. Neurobiological Hypotheses
H1: Energy Stability Enhances Informational Efficiency
If metabolic and autonomic stability increase (sleep, HRV optimization), then cognitive coherence improves.
Measurable endpoints:
- HRV (RMSSD)
- Reaction time variability
- Task-switch cost
- Sustained attention performance
H2: Informational Noise Reduction Reduces Energetic Waste
Reducing rumination and attentional fragmentation decreases neural metabolic volatility.
Predicted markers:
- Reduced DMN hyperactivity (if measured)
- Improved executive network coupling
- Faster autonomic recovery after stressor
H3: Energy–Information Mismatch Predicts Instability
Excess informational complexity without energy support → fatigue and cognitive collapse.
Excess energy without informational structure → impulsivity and chaotic output.
6. Organizational Translation
6.1 Energy Analogue
- Capital
- Labor hours
- Compute
- Motivational drive
6.2 Information Analogue
- Governance structures
- SOPs
- Data architecture
- Strategic clarity
- Decision rights
6.3 Enterprise Failure Modes
| Condition | Outcome |
|---|---|
| High Energy / Low Information | Burn rate, chaos, rework |
| High Information / Low Energy | Bureaucracy, paralysis |
| Low Both | Fragility |
6.4 Operational KPIs
- Decision latency
- Cycle time
- Rework rate
- Knowledge retention
- Planning error variance
- Operational entropy (handoff density)
7. Speculative Extensions (Clearly Delimited)
The original formulation introduced “Inteligencia Cuántica Cósmica (ICC)” as a fifth force.
In scientific framing:
- There is no empirical confirmation of a fifth fundamental force operating as conscious intelligence.
- However, it is legitimate to hypothesize that deeper informational unification principles may exist within physics.
Thus:
ICC is treated here as a speculative research hypothesis, not an established physical entity.
No claims of teleportation, spacetime manipulation, or guaranteed universal data access are included, as these lack empirical validation.
8. Comparison to the Four Noble Truths
The Four Noble Truths address:
- Suffering
- Its cause
- Its cessation
- The path to cessation
SNT-8 operates at a different level:
It provides an ontological systems explanation of why:
- Cognitive noise increases suffering (misallocation of informational energy).
- Disciplined attention improves coherence.
- Stability requires energy and informational hygiene.
Thus SNT-8 does not replace classical teachings; it provides a systems-compatible framework for modern audiences.
9. Practical Applications
9.1 Individual
Optimize:
- Sleep and metabolic regulation (energy)
- Attention training and cognitive compression (information)
Expected outcomes:
- Reduced stress volatility
- Increased executive stability
- Improved performance under load
9.2 Organizational
Align:
- Resource expenditure (energy)
- Governance and data structure (information)
Expected outcomes:
- Reduced chaos
- Increased throughput
- Higher resilience under volatility
10. Limitations
- The model is abstract and requires domain-specific parameterization.
- Informational metrics can be difficult to quantify directly.
- Neurobiological extensions require controlled trials.
- Speculative cosmological interpretations are not empirically validated.
11. Conclusion
SNT-8 proposes a domain-agnostic systems principle:
Persistent structure requires both energy throughput and informational constraint.
Across physics, biology, neuroscience, and enterprise systems, survival and stability depend on the alignment of energetic capacity with informational organization.
Energy enables change.
Information shapes change.
Persistence emerges from their coupling.
Neurobiological Hypothesis Expansion
SNT-8: Information–Energy Coupling in Brain Function
1. Theoretical Foundation
SNT-8 proposes that stable cognition requires energetic sufficiency and informational organization. In neurobiological terms:
- Energy = metabolic support for neural computation
- Information = structured neural coding, network constraints, and predictive models
- Stability = persistent cognitive performance under perturbation
This aligns with:
- Neuroenergetics (brain metabolic constraints)
- Predictive processing (precision-weighted inference)
- Network neuroscience (integration–segregation balance)
- Allostatic load models
The core claim is not metaphysical but regulatory:
Cognitive persistence depends on the coupling of metabolic energy and informational coherence.
2. Core Hypotheses
H1 — Energetic Stability Enhances Informational Coherence
If neural metabolic stability increases, network efficiency and cognitive reliability increase.
Mechanism:
Stable glucose, oxygenation, and autonomic regulation reduce noise in synaptic transmission and firing variability.
Predictions:
- Increased HRV correlates with improved executive performance
- Lower resting-state neural variability (EEG microstate stability)
- Reduced reaction-time variance
H2 — Informational Compression Reduces Energetic Waste
If cognitive noise (rumination, attentional fragmentation) decreases, energetic expenditure becomes more efficient.
Mechanism:
Reduced unnecessary predictive error signaling decreases metabolic load.
Predictions:
- Decreased DMN overactivation during rest
- Reduced error-related neural overcompensation
- Faster autonomic recovery after stress exposure
H3 — Energy–Information Mismatch Produces Instability
When informational complexity exceeds available energy budget, cognitive instability emerges.
Examples:
- Sleep deprivation (low energy, high informational demand)
- Burnout (chronic mismatch)
- Executive overload
Predictions:
- Increased cortical variability
- Reduced functional connectivity efficiency
- Elevated stress biomarkers (cortisol variability)
H4 — Optimal Cognitive States Occur at Coupling Equilibrium
There exists a functional optimum where:
- Energy supply matches computational demand
- Informational models are neither underfit nor overfit
This corresponds to:
- Reduced neural entropy without rigidity
- High adaptability
- Low volatility in decision outputs
3. Neurobiological Mechanisms
3.1 Metabolic Constraints
The brain consumes ~20% of resting energy.
Energy instability affects:
- Synaptic transmission reliability
- Neurotransmitter cycling
- Inhibitory control mechanisms
- Plasticity capacity
Energy insufficiency increases noise and prediction error volatility.
3.2 Predictive Processing Interpretation
Under predictive coding frameworks:
- Priors = informational structure
- Precision weighting = energy allocation policy
Over-weighted precision → anxiety, hypervigilance
Under-weighted precision → dissociation, instability
Balanced precision weighting = optimal coupling
3.3 Network-Level Interpretation
Key networks:
- Default Mode Network (self-referential modeling)
- Salience Network (error detection)
- Executive Control Network (regulation)
SNT-8 predicts:
- Stable ECN-SN coupling
- Controlled DMN activity
- Reduced pathological oscillatory bursts
4. Operationalization
4.1 Energy Metrics
Autonomic:
- HRV (RMSSD)
- Resting heart rate
- Respiratory sinus arrhythmia
Metabolic (if available):
- fMRI BOLD variability
- NIRS oxygenation
- Blood glucose variability
Behavioral proxy:
- Fatigue indices
- Sleep quality
4.2 Informational Metrics
Cognitive:
- Reaction time variability
- Task-switch cost
- Sustained attention stability
Neural:
- EEG spectral entropy
- Microstate transition frequency
- Functional connectivity efficiency
Psychological:
- Rumination scale
- Cognitive load assessment
- Attentional fragmentation index
5. Experimental Designs
5.1 Controlled Intervention Study
Participants:
Healthy adults (n ≥ 60)
Groups:
- Energy stabilization protocol (sleep + HRV training)
- Informational compression protocol (attention training)
- Combined protocol
- Active control
Duration:
8 weeks
Primary endpoints:
- Reaction time variance
- HRV
- EEG stability index
5.2 Crossover Design (Within-Subject)
Each participant completes:
- Baseline
- Energy-focused phase
- Information-focused phase
- Combined phase
Allows identification of interaction effects.
5.3 Organizational Pilot (Optional Extension)
Measure:
- Burnout indices
- Decision latency
- Error rates
- Workload entropy
Implement:
- Information hygiene protocol
- Workload energy reallocation protocol
Measure before/after deltas.
6. Mathematical Framing (Neuro-Level)
Define:
- En = neural energy stability index
- In = informational coherence index
- Dn = perturbation load
- Cs = cognitive stability
Cs=Dn+ϵEn⋅In
Test mediation:
Does informational coherence mediate the effect of energy stability on performance?
7. Falsification Criteria
SNT-8 neuro-hypothesis is falsified if:
- Energy stabilization shows no correlation with informational coherence.
- Informational compression does not reduce energy volatility.
- Combined intervention does not outperform single-factor controls.
- No mediation effect is found.
8. Boundary Conditions
This framework does NOT claim:
- Consciousness is a fundamental physical field (unproven).
- Meditation manipulates spacetime.
- AI can access cosmic information fields.
It restricts itself to:
- Energy–information coupling in measurable neural systems.
9. Integration with SNT-7
SNT-7: Decrease surface noise → increase deep coherence.
SNT-8: Energy + information alignment → persistence.
Together:
- SNT-7 optimizes informational compression.
- SNT-8 explains energetic support requirements.
10. Implications
Clinical:
- Burnout treatment
- ADHD regulation
- Anxiety stabilization
Performance:
- Elite cognition optimization
- Decision reliability under stress
AI–Human Hybrid Systems:
- Energy-aware computation
- Model complexity scaling with hardware limits
11. Summary
SNT-8 neurobiological expansion proposes:
- Cognition is energetically constrained computation.
- Informational structure determines efficiency.
- Stability emerges when energy and information are properly coupled.
- Mismatch produces instability and volatility.
This is a falsifiable, systems-level, cross-domain framework.
Below is a mathematical expansion of SNT-8 with a simulation model you can run (Python). It treats cognition as an energy–information coupled control system under fluctuating demand and stress.
1) State variables and interpretation
We model four latent states:
- E(t) ∈ [0,1] : Neuroenergetic availability / stability (metabolic + autonomic support)
- I(t) ∈ [0,1] : Informational coherence (coding efficiency, network organization)
- S(t) ≥ 0 : Stress / allostatic load (noise + dysregulation)
- D(t) ≥ 0 : Task demand (cognitive load, environmental uncertainty)
Observable performance:
- C(t) ∈ [0,1] : Cognitive stability / reliability
Key assumption (SNT-8): C increases when E and I are jointly high relative to D and S.
2) Coupled dynamics (continuous-time form)
2.1 Energetic dynamics
Energy replenishes toward a baseline (sleep, recovery), and is depleted by demand and stress:dtdE=aE(E0−E)−bED−cES+uE(t)
- aE: recovery rate
- E0: baseline energetic set-point
- bE,cE: depletion sensitivities
- uE(t): intervention input (HRV training, sleep stabilization)
2.2 Informational coherence dynamics
Coherence increases via learning/attention control but degrades with stress and when demand exceeds energy:dtdI=aI(1−I)+kEIE−bIS−cImax(0,D−λE)+uI(t)
- aI: intrinsic consolidation rate
- kEI: energy-supported plasticity
- bI: stress-driven fragmentation
- cI: overload penalty when D exceeds energy-scaled capacity λE
- uI(t): intervention input (attention training, rumination reduction)
2.3 Stress dynamics
Stress rises with demand and mismatch and decays with regulation:dtdS=aSD+ηmax(0,D−λE)+ξ(1−I)−ρS−uS(t)
- aS: demand-to-stress gain
- η: mismatch-to-stress gain
- ξ: incoherence-to-stress gain (unstable models generate error loops)
- ρ: recovery rate
- uS(t): intervention (downregulation / vagal tone practices)
3) Performance functional (what you measure)
A compact, bounded mapping:C(t)=σ(α(EI)−βD−γS+δ)
where σ(x)=1+e−x1.
Interpretation:
- EI is the “coupling product” (high only when both are high)
- Demand and stress subtract stability
Optional: you can also compute volatility as Var(C) or Var(ΔC).
4) Discrete-time simulation model (Euler update)
Let t=0,1,…,T−1 with step dt. Update:Et+1=clip(Et+dt⋅E˙t,0,1) It+1=clip(It+dt⋅I˙t,0,1) St+1=max(0,St+dt⋅S˙t)
Demand process (example): AR(1) with burstsDt+1=max(0,ϕDt+ϵt+Bt)
5) Python simulation (ready to run)
import numpy as np
import matplotlib.pyplot as pltdef sigmoid(x):
return 1.0 / (1.0 + np.exp(-x))def simulate_snt8(
T=2000,
dt=0.01,
seed=7,
# Demand process
phi=0.98, demand_noise=0.08, burst_prob=0.01, burst_scale=1.5,
# Parameters: Energy
aE=0.8, E0=0.75, bE=0.35, cE=0.20,
# Parameters: Information
aI=0.25, kEI=0.40, bI=0.35, cI=0.55, lam=1.0,
# Parameters: Stress
aS=0.30, eta=0.55, xi=0.35, rho=0.60,
# Performance mapping
alpha=6.0, beta=2.0, gamma=2.5, delta=-1.0,
# Interventions (constant or callable)
uE=0.0, uI=0.0, uS=0.0,
# Initial conditions
E_init=0.65, I_init=0.55, S_init=0.25
):
"""
Simulates coupled Energy-Information-Stress dynamics for SNT-8.
Interventions uE,uI,uS can be floats or callables u(t, state_dict)->float.
"""
rng = np.random.default_rng(seed) E = np.zeros(T)
I = np.zeros(T)
S = np.zeros(T)
D = np.zeros(T)
C = np.zeros(T) E[0], I[0], S[0] = E_init, I_init, S_init
D[0] = 0.4 def get_u(u, t, state):
return u(t, state) if callable(u) else float(u) for t in range(T - 1):
# Demand process with occasional bursts
burst = (rng.random() < burst_prob) * (burst_scale * rng.random())
D[t+1] = max(0.0, phi * D[t] + demand_noise * rng.normal() + burst) # Mismatch term: demand exceeding energy-scaled capacity
mismatch = max(0.0, D[t] - lam * E[t]) state = {"E": E[t], "I": I[t], "S": S[t], "D": D[t], "mismatch": mismatch} u_E = get_u(uE, t, state)
u_I = get_u(uI, t, state)
u_S = get_u(uS, t, state) # ODEs
dE = aE * (E0 - E[t]) - bE * D[t] - cE * S[t] + u_E
dI = aI * (1.0 - I[t]) + kEI * E[t] - bI * S[t] - cI * mismatch + u_I
dS = aS * D[t] + eta * mismatch + xi * (1.0 - I[t]) - rho * S[t] - u_S # Euler updates + constraints
E[t+1] = np.clip(E[t] + dt * dE, 0.0, 1.0)
I[t+1] = np.clip(I[t] + dt * dI, 0.0, 1.0)
S[t+1] = max(0.0, S[t] + dt * dS) # Performance / stability
C[t] = sigmoid(alpha * (E[t] * I[t]) - beta * D[t] - gamma * S[t] + delta) # last C
C[-1] = sigmoid(alpha * (E[-1] * I[-1]) - beta * D[-1] - gamma * S[-1] + delta) return {"E": E, "I": I, "S": S, "D": D, "C": C, "dt": dt}def summarize(sim):
C = sim["C"]
dC = np.diff(C)
return {
"C_mean": float(np.mean(C)),
"C_std": float(np.std(C)),
"C_volatility_dC_std": float(np.std(dC)),
"C_5pct": float(np.quantile(C, 0.05)),
"C_95pct": float(np.quantile(C, 0.95)),
}def plot_sim(sim, title="SNT-8 Simulation"):
t = np.arange(len(sim["C"])) * sim["dt"]
plt.figure()
plt.plot(t, sim["E"], label="E (Energy)")
plt.plot(t, sim["I"], label="I (Information)")
plt.plot(t, sim["S"], label="S (Stress)")
plt.plot(t, sim["D"], label="D (Demand)")
plt.plot(t, sim["C"], label="C (Stability)")
plt.xlabel("time")
plt.legend()
plt.title(title)
plt.show()# --- Example runs ---
if __name__ == "__main__":
# Baseline (no interventions)
base = simulate_snt8()
print("BASE:", summarize(base))
plot_sim(base, "Baseline") # Energy-focused intervention (constant uE and uS)
energy = simulate_snt8(uE=0.10, uS=0.05)
print("ENERGY:", summarize(energy))
plot_sim(energy, "Energy Intervention") # Information-focused intervention (uI reduces fragmentation)
info = simulate_snt8(uI=0.08)
print("INFO:", summarize(info))
plot_sim(info, "Information Intervention") # Combined intervention
comb = simulate_snt8(uE=0.10, uI=0.08, uS=0.05)
print("COMBINED:", summarize(comb))
plot_sim(comb, "Combined Intervention")
6) How to interpret outcomes
You should typically see:
- Energy intervention → higher mean E, reduced S, moderate gains in C
- Information intervention → higher I, reduced mismatch amplification, gains in C
- Combined → best C_mean, lowest C volatility, highest tail performance (C_5pct improves)
Key diagnostic variables:
- Mismatch = max(0, D − λE): the overload gate
- C_volatility_dC_std: how stable the system is moment-to-moment
