T12-3-formal: 尺度分离定理的形式化规范
机器验证元数据
type: theorem
verification: machine_ready
dependencies: ["A1-formal.md", "T12-1-formal.md", "T12-2-formal.md"]
verification_points:
- scale_hierarchy_generation
- dynamic_equation_separation
- coupling_strength_calculation
- effective_theory_emergence
- renormalization_group_flow
- critical_exponent_verification
核心定理
定理 T12-3（尺度分离）
ScaleSeparation : Prop ≡
∀system : SelfReferencialSystem .
complete(system) ∧ satisfies_no11(system) →
∃hierarchy : ScaleHierarchy .
emerges_from(hierarchy, system) ∧
φ_structured(hierarchy) ∧
phenomena_separated(hierarchy)
where
ScaleHierarchy : Type = List[ScaleLevel]
ScaleLevel : Type = record {
index : ℕ
time_scale : ℝ
length_scale : ℝ
energy_scale : ℝ
dynamics : DynamicType
phenomena : Set[PhysicalPhenomenon]
}
φ_structured(hierarchy) ≡
∀i . hierarchy[i+1].time_scale = φ × hierarchy[i].time_scale
形式化组件
1. 尺度层次结构定义
ScaleHierarchyGeneration : ℕ → ScaleHierarchy ≡
λmax_levels .
[generate_scale_level(i) | i ← range(max_levels)]
where
generate_scale_level : ℕ → ScaleLevel ≡
λi . ScaleLevel {
index = i,
time_scale = τ₀ × φⁱ,
length_scale = ξ₀ × φ^(i/2),
energy_scale = E₀ × φ^(-i),
dynamics = classify_dynamics(i),
phenomena = classify_phenomena(i)
}
BaseScales : Type ≡
record {
τ₀ : ℝ = 1e-15 # Planck time scale
ξ₀ : ℝ = 1e-35 # Planck length scale
E₀ : ℝ = 1.0 # Base energy scale
}
2. 动力学方程分离
DynamicType : Type ≡
| QuantumDynamics # i ≤ 1: Schrödinger equation
| ClassicalDynamics # 1 < i ≤ 3: Newton equations
| StatisticalDynamics # 3 < i ≤ 6: Boltzmann equation
| FluidDynamics # i > 6: Navier-Stokes equation
DynamicEquation : DynamicType → DifferentialEquation ≡
λdyn_type .
match dyn_type with
| QuantumDynamics →
iℏ(∂ψ/∂t) = Ĥ_quantum(ψ)
| ClassicalDynamics →
d²x/dt² = F_classical(x,t)/m
| StatisticalDynamics →
∂f/∂t + v·∇f = C[f]
| FluidDynamics →
∂u/∂t + (u·∇)u = -∇p/ρ + ν∇²u
SeparationCriterion : ScaleLevel → ScaleLevel → Bool ≡
λlevel1, level2 .
|level1.time_scale - level2.time_scale| > φ × min(level1.time_scale, level2.time_scale)
3. 尺度间耦合强度
InterScaleCoupling : ScaleLevel → ScaleLevel → ℝ ≡
λlevel1, level2 .
let Δi = |level1.index - level2.index| in
if Δi > 1 then 0.0 # Non-adjacent scales don't couple
else
let base_coupling = φ^(-Δi) in
let energy_gap = |level1.energy_scale - level2.energy_scale| in
let suppression = exp(-energy_gap / thermal_scale) in
base_coupling × suppression
CouplingMatrix : ScaleHierarchy → Matrix[ℝ] ≡
λhierarchy .
[[InterScaleCoupling(hierarchy[i], hierarchy[j])
for j in range(|hierarchy|)]
for i in range(|hierarchy|)]
CouplingConstraint : ScaleHierarchy → Bool ≡
λhierarchy .
let coupling_matrix = CouplingMatrix(hierarchy) in
∀i,j . coupling_matrix[i][j] ≤ φ^(-|i-j|)
4. 有效理论涌现
EffectiveTheory : Type ≡
record {
theory_type : TheoryType
governing_equations : Set[DifferentialEquation]
degrees_of_freedom : Set[Variable]
symmetries : Set[Symmetry]
characteristic_scales : (ℝ, ℝ, ℝ) # (time, length, energy)
}
TheoryType : Type ≡
| QuantumFieldTheory
| ClassicalMechanics
| StatisticalMechanics
| ContinuumMechanics
EffectiveTheoryEmergence : ScaleLevel → EffectiveTheory ≡
λlevel .
match level.dynamics with
| QuantumDynamics →
EffectiveTheory {
theory_type = QuantumFieldTheory,
governing_equations = {Schrödinger, Dirac, Klein-Gordon},
degrees_of_freedom = {quantum_states, field_operators},
symmetries = {U(1), SU(2), Lorentz},
characteristic_scales = (level.time_scale, level.length_scale, level.energy_scale)
}
| ClassicalDynamics →
EffectiveTheory {
theory_type = ClassicalMechanics,
governing_equations = {Newton, Hamilton, Lagrange},
degrees_of_freedom = {position, momentum},
symmetries = {Galilean, rotational, translational},
characteristic_scales = (level.time_scale, level.length_scale, level.energy_scale)
}
# ... additional cases
TheoryCompleteness : EffectiveTheory → ScaleLevel → Bool ≡
λtheory, level .
all_phenomena_explained(theory, level.phenomena) ∧
scale_consistency(theory.characteristic_scales, level) ∧
symmetry_consistency(theory.symmetries, level)
5. 重整化群流
RenormalizationGroup : Type ≡
record {
beta_functions : List[ℝ → ℝ]
anomalous_dimensions : List[ℝ]
fixed_points : List[ℝ]
flow_trajectories : List[ℝ → ℝ]
}
PhiBetaFunction : ℝ → ℝ ≡
λcoupling .
-φ × coupling + (coupling³ / φ²) + O(coupling⁵)
RGFlow : ℝ → List[ℝ] → List[ℝ] ≡
λinitial_coupling, scale_range .
let flow_step = λ(coupling, scale) .
let β = PhiBetaFunction(coupling) in
coupling + β × (Δ log scale)
in
fold_left(flow_step, initial_coupling, scale_range)
FixedPointAnalysis : RenormalizationGroup → List[FixedPoint] ≡
λrg .
[λ* | λ* ← candidate_values, PhiBetaFunction(λ*) = 0]
where
FixedPoint : Type = record {
value : ℝ
stability : StabilityType
universality_class : UniversalityClass
}
6. 临界指数和φ-普适类
CriticalExponents : Type ≡
record {
ν : ℝ = 1/φ # Correlation length exponent
β : ℝ = 1/φ² # Order parameter exponent
γ : ℝ = (φ+1)/φ # Susceptibility exponent
δ : ℝ = φ+1 # Critical isotherm exponent
α : ℝ = 2-φ # Specific heat exponent
η : ℝ = 2-2/φ # Anomalous dimension
}
PhiUniversalityClass : UniversalityClass ≡
UniversalityClass {
name = "Phi-Universality",
critical_exponents = CriticalExponents(),
dimensionality = d,
symmetry = φ_symmetry,
description = "All systems with φ-structured scale separation"
}
ScalingLaw : ℝ → ℝ → ℝ → ℝ ≡
λobservable, control_parameter, critical_point .
let t = (control_parameter - critical_point) / critical_point in
observable_scaling_function(|t|^exponent)
FiniteSizeScaling : ℝ → ℝ → ℝ ≡
λsystem_size, correlation_length .
universal_scaling_function(system_size / correlation_length)
算法规范
尺度层次生成算法
GenerateScaleHierarchy : Algorithm ≡
Input: max_levels : ℕ, base_scales : BaseScales
Output: hierarchy : ScaleHierarchy
Process:
1. φ = (1 + √5) / 2
2. hierarchy = []
3.
4. for i in range(max_levels):
level = ScaleLevel(
index = i,
time_scale = base_scales.τ₀ × φ^i,
length_scale = base_scales.ξ₀ × φ^(i/2),
energy_scale = base_scales.E₀ × φ^(-i),
dynamics = classify_dynamics_by_scale(i),
phenomena = classify_phenomena_by_scale(i)
)
hierarchy.append(level)
5. verify_phi_scaling(hierarchy)
6. return hierarchy
Invariants:
- ∀i . hierarchy[i+1].time_scale / hierarchy[i].time_scale = φ
- ∀i . hierarchy[i+1].energy_scale / hierarchy[i].energy_scale = 1/φ
- scale separation maintained across all levels
动力学分离验证算法
VerifyDynamicSeparation : Algorithm ≡
Input: hierarchy : ScaleHierarchy
Output: separation_verified : Bool
Process:
1. for each adjacent pair (level_i, level_{i+1}) in hierarchy:
# Check time scale separation
time_ratio = level_{i+1}.time_scale / level_i.time_scale
assert abs(time_ratio - φ) < tolerance
# Check dynamic type transition
if level_i.dynamics ≠ level_{i+1}.dynamics:
verify_transition_consistency(level_i, level_{i+1})
# Check phenomena separation
overlap = intersection(level_i.phenomena, level_{i+1}.phenomena)
assert |overlap| / |union(level_i.phenomena, level_{i+1}.phenomena)| < 0.2
2. return all_separations_verified
有效理论涌现算法
EmergentTheoryConstruction : Algorithm ≡
Input: scale_level : ScaleLevel
Output: effective_theory : EffectiveTheory
Process:
1. # Determine theory type based on scale
2. if scale_level.time_scale < quantum_classical_boundary:
theory_type = QuantumFieldTheory
governing_eqs = construct_quantum_equations(scale_level)
dof = extract_quantum_degrees_of_freedom(scale_level)
3. elif scale_level.time_scale < classical_statistical_boundary:
theory_type = ClassicalMechanics
governing_eqs = construct_classical_equations(scale_level)
dof = extract_classical_degrees_of_freedom(scale_level)
4. else:
theory_type = StatisticalMechanics
governing_eqs = construct_statistical_equations(scale_level)
dof = extract_collective_degrees_of_freedom(scale_level)
5. # Extract relevant symmetries
6. symmetries = identify_symmetries(scale_level, theory_type)
7. # Construct effective theory
8. effective_theory = EffectiveTheory(
theory_type, governing_eqs, dof, symmetries,
(scale_level.time_scale, scale_level.length_scale, scale_level.energy_scale)
)
9. # Verify completeness
10. assert verify_theory_completeness(effective_theory, scale_level)
11. return effective_theory
重整化群分析算法
RenormalizationGroupAnalysis : Algorithm ≡
Input: initial_coupling : ℝ, scale_range : List[ℝ]
Output: rg_analysis : RGAnalysisResult
Process:
1. φ = (1 + √5) / 2
2. coupling_evolution = [initial_coupling]
3. current_coupling = initial_coupling
4.
5. for scale in scale_range:
# Compute β-function
β = -φ × current_coupling + (current_coupling³ / φ²)
# Evolve coupling
d_log_scale = log(scale / previous_scale) if previous_scale else 0
current_coupling += β × d_log_scale
coupling_evolution.append(current_coupling)
previous_scale = scale
6. # Find fixed points
7. fixed_points = find_zeros(PhiBetaFunction, search_range=(-5, 5))
8.
9. # Analyze stability
10. stability_analysis = []
11. for fp in fixed_points:
β_prime = d_PhiBetaFunction_d_coupling(fp)
if β_prime < 0:
stability = "UV_attractive"
elif β_prime > 0:
stability = "IR_attractive"
else:
stability = "marginal"
stability_analysis.append((fp, stability))
12. return RGAnalysisResult(
coupling_evolution, fixed_points, stability_analysis
)
φ-普适类验证算法
VerifyPhiUniversalityClass : Algorithm ≡
Input: critical_data : List[CriticalMeasurement]
Output: universality_verification : UniversalityVerification
Process:
1. φ = (1 + √5) / 2
2. theoretical_exponents = CriticalExponents()
3.
4. # Fit experimental critical exponents
5. fitted_exponents = {}
6.
7. # Correlation length exponent ν
8. correlation_data = [(d.control_param, d.correlation_length) for d in critical_data]
9. ν_fitted = fit_power_law_exponent(correlation_data, critical_point)
10. fitted_exponents["ν"] = ν_fitted
11.
12. # Order parameter exponent β
13. order_data = [(d.control_param, d.order_parameter) for d in critical_data]
14. β_fitted = fit_power_law_exponent(order_data, critical_point)
15. fitted_exponents["β"] = β_fitted
16.
17. # Similar fits for other exponents...
18.
19. # Compare with φ-theoretical predictions
20. verification_results = {}
21. for exponent_name in ["ν", "β", "γ", "δ", "α"]:
theoretical_value = getattr(theoretical_exponents, exponent_name)
fitted_value = fitted_exponents[exponent_name]
error = abs(fitted_value - theoretical_value)
relative_error = error / theoretical_value
verification_results[exponent_name] = {
"theoretical": theoretical_value,
"fitted": fitted_value,
"error": error,
"relative_error": relative_error,
"verified": relative_error < 0.15 # 15% tolerance
}
22. # Overall verification
23. overall_verified = all(v["verified"] for v in verification_results.values())
24.
25. return UniversalityVerification(
verification_results, overall_verified, fitted_exponents
)
数学性质验证
性质1：φ-尺度分离
PhiScaleSeparation : Prop ≡
∀hierarchy : ScaleHierarchy, i : ℕ .
i+1 < |hierarchy| →
hierarchy[i+1].time_scale / hierarchy[i].time_scale = φ ∧
hierarchy[i+1].energy_scale / hierarchy[i].energy_scale = 1/φ
ProofSketch:
By construction of ScaleHierarchy
time_scale[i] = τ₀ × φⁱ
Therefore: time_scale[i+1] / time_scale[i] = φ^(i+1) / φⁱ = φ □
性质2：动力学完备性
DynamicCompleteness : Prop ≡
∀level : ScaleLevel .
∃theory : EffectiveTheory .
emerges_from(theory, level) ∧
explains_all_phenomena(theory, level.phenomena) ∧
scale_consistent(theory, level)
ProofSketch:
For each scale range, construct appropriate effective theory
Quantum scales → QFT, Classical scales → Newtonian mechanics, etc.
Completeness follows from φ-structured emergence □
性质3：重整化群φ-流
RGPhiFlow : Prop ≡
∀λ : ℝ . β(λ) = -φλ + λ³/φ² + O(λ⁵) →
fixed_points(β) = {0, ±√(φ³), ...} ∧
universality_class = PhiUniversalityClass
ProofSketch:
β(λ*) = 0 ⟹ -φλ* + (λ*)³/φ² = 0
⟹ λ* = 0 or λ* = ±√(φ³)
φ-structure determines universality class □
性质4：临界指数关系
CriticalExponentRelations : Prop ≡
ν = 1/φ ∧ β = 1/φ² ∧ γ = (φ+1)/φ →
scaling_laws_satisfied ∧
hyperscaling_relations_hold ∧
Josephson_identities_verified
where hyperscaling includes:
2β + γ = 2 - α
γ = ν(2 - η)
δ = 1 + γ/β
验证检查点
1. 尺度层次生成验证
def verify_scale_hierarchy_generation(max_levels):
"""验证尺度层次生成"""
φ = (1 + math.sqrt(5)) / 2
hierarchy = generate_scale_hierarchy(max_levels)
# Verify φ-scaling
for i in range(len(hierarchy) - 1):
time_ratio = hierarchy[i+1].time_scale / hierarchy[i].time_scale
assert abs(time_ratio - φ) < 1e-10, \
f"Time scale ratio {time_ratio:.6f} ≠ φ = {φ:.6f}"
energy_ratio = hierarchy[i+1].energy_scale / hierarchy[i].energy_scale
assert abs(energy_ratio - 1/φ) < 1e-10, \
f"Energy scale ratio {energy_ratio:.6f} ≠ 1/φ = {1/φ:.6f}"
# Verify scale separation
for i in range(len(hierarchy) - 1):
time_separation = hierarchy[i+1].time_scale - hierarchy[i].time_scale
min_time = min(hierarchy[i].time_scale, hierarchy[i+1].time_scale)
assert time_separation > φ * min_time, \
f"Insufficient time scale separation at level {i}"
return True
2. 动力学方程分离验证
def verify_dynamic_equation_separation(hierarchy):
"""验证动力学方程分离"""
for i, level in enumerate(hierarchy):
expected_dynamics = classify_dynamics_by_scale(i)
assert level.dynamics == expected_dynamics, \
f"Level {i}: Expected {expected_dynamics}, got {level.dynamics}"
# Verify appropriate equations
effective_theory = construct_effective_theory(level)
assert verify_equation_consistency(effective_theory, level.dynamics), \
f"Level {i}: Inconsistent equations for {level.dynamics}"
# Verify transitions between scales
for i in range(len(hierarchy) - 1):
if hierarchy[i].dynamics != hierarchy[i+1].dynamics:
assert verify_smooth_transition(hierarchy[i], hierarchy[i+1]), \
f"Non-smooth transition between levels {i} and {i+1}"
return True
3. 耦合强度计算验证
def verify_coupling_strength_calculation(hierarchy):
"""验证耦合强度计算"""
φ = (1 + math.sqrt(5)) / 2
for i in range(len(hierarchy)):
for j in range(len(hierarchy)):
coupling = calculate_inter_scale_coupling(hierarchy[i], hierarchy[j])
if abs(i - j) > 1:
# Non-adjacent scales should not couple
assert coupling == 0.0, \
f"Non-zero coupling {coupling} between non-adjacent levels {i}, {j}"
elif abs(i - j) == 1:
# Adjacent scales should have φ-suppressed coupling
expected_coupling = φ ** (-1)
assert coupling <= expected_coupling, \
f"Coupling {coupling} exceeds φ-bound {expected_coupling}"
assert coupling > 0, \
f"Zero coupling between adjacent levels {i}, {j}"
else: # i == j
# Self-coupling
assert coupling >= 0, f"Negative self-coupling at level {i}"
return True
4. 有效理论涌现验证
def verify_effective_theory_emergence(hierarchy):
"""验证有效理论涌现"""
for level in hierarchy:
effective_theory = construct_effective_theory(level)
# Verify theory type matches scale
if level.time_scale < 1e-12: # Quantum scale
assert effective_theory.theory_type == QuantumFieldTheory, \
f"Wrong theory type for quantum scale: {effective_theory.theory_type}"
elif level.time_scale < 1e-6: # Classical scale
assert effective_theory.theory_type == ClassicalMechanics, \
f"Wrong theory type for classical scale: {effective_theory.theory_type}"
else: # Statistical scale
assert effective_theory.theory_type in [StatisticalMechanics, ContinuumMechanics], \
f"Wrong theory type for statistical scale: {effective_theory.theory_type}"
# Verify completeness
assert verify_theory_completeness(effective_theory, level), \
f"Incomplete theory at level {level.index}"
# Verify scale consistency
theory_scales = effective_theory.characteristic_scales
assert abs(theory_scales[0] - level.time_scale) / level.time_scale < 0.01, \
"Time scale mismatch between theory and level"
return True
5. 重整化群流验证
def verify_renormalization_group_flow(scale_range):
"""验证重整化群流"""
φ = (1 + math.sqrt(5)) / 2
# Test multiple initial couplings
initial_couplings = [-2.0, -0.5, 0.0, 0.5, 2.0]
for λ₀ in initial_couplings:
flow_data = compute_rg_flow(λ₀, scale_range)
# Verify β-function
for data_point in flow_data:
λ = data_point['coupling']
β_computed = data_point['beta_function']
β_theoretical = -φ * λ + (λ**3) / (φ**2)
assert abs(β_computed - β_theoretical) < 1e-6, \
f"β-function error: computed={β_computed:.6f}, theoretical={β_theoretical:.6f}"
# Verify fixed points
if abs(λ₀) < 0.1: # Near trivial fixed point
final_coupling = flow_data[-1]['coupling']
assert abs(final_coupling) < abs(λ₀) + 0.1, \
"Coupling should flow toward fixed point"
# Find and verify fixed points
fixed_points = find_fixed_points(lambda λ: -φ * λ + (λ**3) / (φ**2))
# Verify trivial fixed point
assert any(abs(fp) < 1e-6 for fp in fixed_points), \
"Trivial fixed point λ*=0 not found"
# Verify non-trivial fixed points
expected_nontrivial = math.sqrt(φ**3)
assert any(abs(abs(fp) - expected_nontrivial) < 0.01 for fp in fixed_points), \
f"Non-trivial fixed point λ*=±√(φ³)=±{expected_nontrivial:.3f} not found"
return True
6. 临界指数验证
def verify_critical_exponent_verification(critical_systems_data):
"""验证临界指数"""
φ = (1 + math.sqrt(5)) / 2
# Theoretical φ-universality predictions
theoretical_exponents = {
'ν': 1/φ, # ≈ 0.618
'β': 1/(φ**2), # ≈ 0.382
'γ': (φ+1)/φ, # ≈ 1.618
'δ': φ+1, # ≈ 2.618
'α': 2-φ # ≈ 0.382
}
for system_name, data in critical_systems_data.items():
fitted_exponents = fit_critical_exponents(data)
for exponent_name, theoretical_value in theoretical_exponents.items():
if exponent_name in fitted_exponents:
fitted_value = fitted_exponents[exponent_name]
relative_error = abs(fitted_value - theoretical_value) / theoretical_value
print(f"{system_name} {exponent_name}: fitted={fitted_value:.3f}, "
f"theoretical={theoretical_value:.3f}, error={relative_error:.3f}")
# Allow 20% tolerance for complex many-body systems
assert relative_error < 0.2, \
f"{system_name}: {exponent_name} error {relative_error:.3f} > 20%"
# Verify hyperscaling relations
if all(exp in fitted_exponents for exp in ['α', 'β', 'γ', 'ν', 'δ']):
verify_hyperscaling_relations(fitted_exponents)
return True
def verify_hyperscaling_relations(exponents):
"""验证超标度关系"""
α, β, γ, ν, δ = [exponents[k] for k in ['α', 'β', 'γ', 'ν', 'δ']]
# Rushbrooke inequality: α + 2β + γ ≥ 2
rushbrooke = α + 2*β + γ
assert rushbrooke >= 1.9, f"Rushbrooke relation violated: {rushbrooke:.3f} < 2"
# Josephson identity: δ = 1 + γ/β
josephson_lhs = δ
josephson_rhs = 1 + γ/β
assert abs(josephson_lhs - josephson_rhs) < 0.1, \
f"Josephson identity violated: {josephson_lhs:.3f} ≠ {josephson_rhs:.3f}"
return True
实用函数
def analyze_multiscale_system(phenomena_list, time_scales, length_scales):
"""分析多尺度系统"""
φ = (1 + math.sqrt(5)) / 2
# Classify phenomena by scale
scale_classification = {}
for i, (phenomenon, τ, ξ) in enumerate(zip(phenomena_list, time_scales, length_scales)):
# Find appropriate scale level
level = int(math.log(τ / 1e-15, φ)) # τ₀ = 1e-15
if level not in scale_classification:
scale_classification[level] = []
scale_classification[level].append({
'phenomenon': phenomenon,
'time_scale': τ,
'length_scale': ξ,
'predicted_dynamics': classify_dynamics_by_scale(level)
})
return scale_classification
def predict_emergence_conditions(target_phenomenon, system_parameters):
"""预测涌现条件"""
φ = (1 + math.sqrt(5)) / 2
# Determine required scale level for phenomenon
required_level = phenomenon_to_scale_level(target_phenomenon)
required_time_scale = 1e-15 * (φ ** required_level)
required_length_scale = 1e-35 * (φ ** (required_level/2))
# Check if system parameters support emergence
system_time_scale = estimate_system_time_scale(system_parameters)
system_length_scale = estimate_system_length_scale(system_parameters)
emergence_probability = calculate_emergence_probability(
system_time_scale, required_time_scale,
system_length_scale, required_length_scale
)
return {
'target_phenomenon': target_phenomenon,
'required_level': required_level,
'required_scales': (required_time_scale, required_length_scale),
'system_scales': (system_time_scale, system_length_scale),
'emergence_probability': emergence_probability,
'recommendations': generate_optimization_recommendations(
system_parameters, required_level
)
}
def design_scale_separation_experiment(phenomenon_pairs):
"""设计尺度分离实验"""
experiments = []
for phenomenon1, phenomenon2 in phenomenon_pairs:
level1 = phenomenon_to_scale_level(phenomenon1)
level2 = phenomenon_to_scale_level(phenomenon2)
if abs(level1 - level2) < 2:
# Phenomena too close in scale
continue
φ = (1 + math.sqrt(5)) / 2
scale_ratio = φ ** abs(level1 - level2)
experiment = {
'phenomena': (phenomenon1, phenomenon2),
'scale_levels': (level1, level2),
'predicted_separation_ratio': scale_ratio,
'measurement_strategy': design_measurement_strategy(level1, level2),
'expected_coupling': φ ** (-abs(level1 - level2)),
'resolution_requirements': calculate_required_resolution(level1, level2)
}
experiments.append(experiment)
return experiments
与其他理论的联系
依赖关系
- A1: 自指完备系统必然熵增（基础公理）
- T12-1: 量子-经典过渡（微观基础）
- T12-2: 宏观涌现（中观结构）
支撑的理论
- 重整化群理论的φ基础
- 临界现象的普适性分类
- 有效场论的涌现机制
- 多尺度建模的数学基础