class PhiNumber:
def __init__(self, value: float):
self.phi = (1 + np.sqrt(5)) / 2
self.value = float(value)
def to_fibonacci_basis(self) -> List[int]:
"""转换为Fibonacci基表示（Zeckendorf表示）"""
def verify_no_11(self) -> bool:
"""验证表示中无连续的11"""
class EntropyFunction:
def __init__(self, system: 'SelfReferentialSystem'):
self.system = system
self.phi = (1 + np.sqrt(5)) / 2
self.k0 = 1.0 # 基准速率常数
def compute_entropy(self, time: int) -> 'PhiNumber':
"""计算时刻t的系统熵"""
def entropy_rate(self, time: int) -> 'PhiNumber':
"""计算熵增速率 dH/dt"""
def recursive_depth(self, time: int) -> int:
"""计算递归深度d(t)"""
class RecursiveDepth:
def __init__(self):
self.depths = {0: 0, 1: 1} # 初始条件
def compute_depth(self, time: int) -> int:
"""计算时刻t的递归深度（Fibonacci增长）"""
if time in self.depths:
return self.depths[time]
# Fibonacci递归：d(t+1) = d(t) + d(t-1)
depth = self.compute_depth(time-1) + self.compute_depth(time-2)
self.depths[time] = depth
return depth
def verify_fibonacci_growth(self) -> bool:
"""验证递归深度的Fibonacci增长性"""
class No11Modulation:
def __init__(self, epsilon: float = 0.01, T: float = 1.0):
self.epsilon = epsilon # 约束强度
self.T = T # 特征时间尺度
def theta_factor(self, time: float) -> float:
"""计算no-11约束因子Θ(t)"""
theta = 1.0
# Fibonacci频率的调制
fib_prev, fib_curr = 1, 1
for n in range(1, 20): # 前20个Fibonacci数
theta -= self.epsilon * np.sin(2 * np.pi * fib_curr * time / self.T) / fib_curr
fib_prev, fib_curr = fib_curr, fib_prev + fib_curr
return theta
def verify_bounds(self) -> bool:
"""验证|Θ(t) - 1| ≤ ε"""
class FibonacciGenerator:
def __init__(self):
self.cache = {0: 0, 1: 1, 2: 1}
def fibonacci(self, n: int) -> int:
"""生成第n个Fibonacci数"""
if n in self.cache:
return self.cache[n]
fib = self.fibonacci(n-1) + self.fibonacci(n-2)
self.cache[n] = fib
return fib
def fibonacci_sequence(self, max_n: int) -> List[int]:
"""生成Fibonacci序列"""
def is_fibonacci(self, num: int) -> bool:
"""判断是否为Fibonacci数"""
class EntropyRateCalculator:
def __init__(self, k0: float = 1.0):
self.k0 = k0
self.phi = (1 + np.sqrt(5)) / 2
self.depth_calc = RecursiveDepth()
self.modulation = No11Modulation()
def compute_rate(self, time: float) -> 'PhiNumber':
"""计算熵增速率 dH/dt = k0 * φ^d(t) * Θ(t)"""
d_t = self.depth_calc.compute_depth(int(time))
theta_t = self.modulation.theta_factor(time)
rate = self.k0 * (self.phi ** d_t) * theta_t
return PhiNumber(rate)
def verify_bounds(self, time: float) -> bool:
"""验证速率在理论界限内"""
def asymptotic_behavior(self, time: float) -> 'PhiNumber':
"""计算渐近行为"""
class EntropyEvolution:
def __init__(self, H0: 'PhiNumber'):
self.H0 = H0 # 初始熵
self.rate_calc = EntropyRateCalculator()
self.history = [(0, H0)]
def evolve(self, time_steps: int, dt: float = 0.01) -> List[Tuple[float, 'PhiNumber']]:
"""演化系统熵"""
def integrate_entropy(self, t_start: float, t_end: float) -> 'PhiNumber':
"""积分计算累积熵变"""
def find_phase_transitions(self) -> List[float]:
"""找出相变点（熵增速率突变）"""
class EmergentTime:
def __init__(self, entropy_evolution: 'EntropyEvolution'):
self.entropy_evolution = entropy_evolution
def proper_time_rate(self, coordinate_time: float) -> 'PhiNumber':
"""计算固有时流逝率 dτ/dt = 1/(dH/dt)"""
def time_dilation_factor(self, t1: float, t2: float) -> 'PhiNumber':
"""计算两个时刻间的时间膨胀因子"""
class InformationRate:
def __init__(self, entropy_rate: 'EntropyRateCalculator'):
self.entropy_rate = entropy_rate
def max_processing_rate(self, time: float) -> 'PhiNumber':
"""最大信息处理速率 dI/dt ≤ dH/dt"""
def channel_capacity(self, time: float) -> 'PhiNumber':
"""信道容量"""
class ComplexityEvolution:
def __init__(self, alpha: float = 0.5):
self.alpha = alpha # 复杂度-熵转换因子
self.entropy_rate = EntropyRateCalculator()
def complexity_rate(self, time: float) -> 'PhiNumber':
"""复杂度增长率 dC/dt = α * dH/dt"""
def total_complexity(self, time: float) -> 'PhiNumber':
"""累积复杂度"""
class EntropyDifferentialEquation:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def second_order_eq(self, t: float, H: float, dH_dt: float) -> float:
"""二阶微分方程：d²H/dt² = dH/dt * (log φ + dΘ/dt/Θ)"""
def solve_ivp(self, t_span: Tuple[float, float],
initial_conditions: Tuple[float, float]) -> 'Solution':
"""求解初值问题"""
class EntropyVariational:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def lagrangian(self, H: float, dH_dt: float) -> float:
"""拉格朗日量 L(H, dH/dt)"""
def action(self, path: List[Tuple[float, float]], dt: float) -> float:
"""作用量 S = ∫[H*dH/dt - L]dt"""
def find_extremal_path(self, boundary_conditions: Tuple) -> List[Tuple[float, float]]:
"""寻找使作用量极值的路径"""
class BlackHoleEntropy:
def __init__(self, mass: float):
self.mass = mass
self.entropy_rate = EntropyRateCalculator()
def bekenstein_hawking_rate(self, time: float) -> 'PhiNumber':
"""黑洞熵增速率"""
def hawking_temperature(self) -> 'PhiNumber':
"""Hawking温度"""
class QuantumDecoherence:
def __init__(self, n_qubits: int, temperature: float):
self.n_qubits = n_qubits
self.temperature = temperature
self.phi = (1 + np.sqrt(5)) / 2
def decoherence_rate_bound(self) -> 'PhiNumber':
"""退相干率下界 γ ≥ k_B*T/ħ * φ^(-n)"""
class BiologicalComplexity:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def complexity_growth_rate(self, generation: int) -> 'PhiNumber':
"""生物复杂度增长率 dC_bio/dt ∝ φ^generation"""
class AsymptoticAnalysis:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
self.tau_phi = np.log(self.phi) / np.log(1 + 1/self.phi)
def long_time_behavior(self, time: float) -> 'PhiNumber':
"""长时渐近行为 dH/dt ~ k0 * φ^(t/τ_φ)"""
def oscillation_periods(self) -> List[float]:
"""主要振荡周期"""
def phase_transition_points(self, T: float) -> List[float]:
"""相变点 t_c = T*F_n/(2π)"""
def verify_fibonacci_growth(depth_sequence: List[int]) -> bool:
"""验证递归深度的Fibonacci增长"""
def verify_entropy_bounds(rate_history: List[float], epsilon: float) -> bool:
"""验证熵增速率的上下界"""
def verify_no_11_constraint(evolution: List['PhiNumber']) -> bool:
"""验证演化过程满足no-11约束"""
def check_numerical_stability(evolution: 'EntropyEvolution') -> bool:
"""检查数值计算的稳定性"""
def estimate_truncation_error(n_terms: int) -> float:
"""估计级数截断误差"""
# 基础常数
PHI = (1 + np.sqrt(5)) / 2 # 黄金分割率
TAU_PHI = np.log(PHI) / np.log(1 + 1/PHI) # 特征时间 ≈ 1.44
# 物理常数（归一化单位）
K_B = 1.0 # Boltzmann常数
HBAR = 1.0 # 约化Planck常数
C = 1.0 # 光速
G = 1.0 # 引力常数
# 模型参数
K0_DEFAULT = 1.0 # 默认基准速率
EPSILON_DEFAULT = 0.01 # 默认约束强度
T_DEFAULT = 1.0 # 默认特征时间尺度
class EntropyRateError(Exception):
"""熵增速率计算错误基类"""
class NegativeDepthError(EntropyRateError):
"""负递归深度错误"""
class ConstraintViolationError(EntropyRateError):
"""约束违反错误"""
class ConvergenceError(EntropyRateError):
"""数值收敛错误"""