class LocalSystem:
def __init__(self, boundary: 'Boundary', content: Set[Any]):
self.boundary = boundary
self.content = content
self.phi = (1 + np.sqrt(5)) / 2
def entropy(self) -> 'PhiNumber':
"""计算局部系统的熵"""
def is_causally_closed(self) -> bool:
"""检查因果闭合性"""
def interface_entropy(self) -> 'PhiNumber':
"""计算界面熵"""
class Boundary:
def __init__(self, surface_elements: List['SurfaceElement']):
self.elements = surface_elements
self.phi = (1 + np.sqrt(5)) / 2
def area(self) -> 'PhiNumber':
"""计算边界面积"""
def degrees_of_freedom(self) -> int:
"""边界自由度数"""
def verify_no_11_constraint(self) -> bool:
"""验证边界编码满足no-11约束"""
def entanglement_entropy(self) -> 'PhiNumber':
"""计算跨边界纠缠熵"""
class EntropyFlow:
def __init__(self, local_system: 'LocalSystem'):
self.system = local_system
self.phi = (1 + np.sqrt(5)) / 2
def inflow_rate(self, time: float) -> 'PhiNumber':
"""熵流入率 J_in"""
def outflow_rate(self, time: float) -> 'PhiNumber':
"""熵流出率 J_out"""
def local_production_rate(self, time: float) -> 'PhiNumber':
"""局部熵产生率 σ_local ≥ 0"""
def net_flow(self, time: float) -> 'PhiNumber':
"""净熵流 = J_in - J_out + σ_local"""
class MinimumCostCalculator:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def minimum_environmental_cost(self,
local_decrease: 'PhiNumber') -> 'PhiNumber':
"""计算局部熵减的最小环境代价"""
if local_decrease >= 0:
raise ValueError("Local entropy must decrease")
# ΔH_env^min = φ * |ΔH_local| + ΔH_process
min_cost = self.phi * abs(local_decrease.value)
process_cost = self.process_entropy_cost(local_decrease)
return PhiNumber(min_cost + process_cost.value)
def process_entropy_cost(self, local_decrease: 'PhiNumber') -> 'PhiNumber':
"""计算实现熵减过程本身的熵成本"""
# 基于信息处理需求
n_bits = self.information_requirement(local_decrease)
return PhiNumber(n_bits * np.log(2))
def information_requirement(self, entropy_change: 'PhiNumber') -> float:
"""计算所需的信息处理量（比特）"""
return abs(entropy_change.value) / np.log(2)
class EntropyBalanceVerifier:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def verify_total_increase(self, local_change: 'PhiNumber',
env_change: 'PhiNumber') -> bool:
"""验证总熵增 ΔH_total > 0"""
total = local_change + env_change
return total > 0
def verify_minimum_condition(self, local_change: 'PhiNumber',
env_change: 'PhiNumber') -> bool:
"""验证环境熵增满足最小条件"""
if local_change >= 0:
return True # 无需验证
min_required = self.phi * abs(local_change.value)
return env_change.value >= min_required
def calculate_efficiency(self, local_change: 'PhiNumber',
env_change: 'PhiNumber') -> float:
"""计算熵减效率"""
if local_change >= 0 or env_change <= 0:
return 0
return abs(local_change.value) / env_change.value
class MaxwellDemon:
def __init__(self, temperature: float):
self.temperature = temperature
self.phi = (1 + np.sqrt(5)) / 2
self.k_B = 1.38064852e-23 # Boltzmann常数
self.memory = []
def measure_particle(self, particle: 'Particle') -> 'PhiNumber':
"""测量粒子状态的熵成本"""
precision = particle.required_precision()
info_bits = np.log2(precision)
# 信息获取成本：ΔH_measure = k_B*T*ln(2)*φ^n
entropy_cost = self.k_B * self.temperature * np.log(2) * \
(self.phi ** info_bits)
# 存储信息
self.memory.append(particle.state)
return PhiNumber(entropy_cost)
def sort_particles(self, particles: List['Particle']) -> Tuple['PhiNumber', 'PhiNumber']:
"""分离快慢粒子，返回(气体熵减，妖熵增)"""
gas_entropy_decrease = PhiNumber(0)
demon_entropy_increase = PhiNumber(0)
for particle in particles:
# 测量成本
measure_cost = self.measure_particle(particle)
demon_entropy_increase += measure_cost
# 分离导致的熵减
if self.should_let_through(particle):
gas_entropy_decrease -= PhiNumber(self.k_B * np.log(2))
return gas_entropy_decrease, demon_entropy_increase
def erase_memory(self) -> 'PhiNumber':
"""擦除记忆的熵成本"""
n_bits = len(self.memory)
# Landauer原理：ΔH_erase = k_B*T*ln(2)*φ per bit
erase_cost = n_bits * self.k_B * self.temperature * np.log(2) * self.phi
self.memory.clear()
return PhiNumber(erase_cost)
def net_entropy_change(self, particles: List['Particle']) -> 'PhiNumber':
"""计算总熵变（应该>0）"""
gas_decrease, demon_increase = self.sort_particles(particles)
erase_cost = self.erase_memory()
total = gas_decrease + demon_increase + erase_cost
return total
class LivingSystem:
def __init__(self, volume: float, temperature: float):
self.volume = volume
self.temperature = temperature
self.phi = (1 + np.sqrt(5)) / 2
self.internal_entropy = PhiNumber(0)
def metabolic_gradient(self) -> 'PhiNumber':
"""代谢梯度（化学势差）"""
# ∇μ > μ_c^φ = k_B*T*φ
def maintain_low_entropy(self, time_step: float) -> Dict[str, 'PhiNumber']:
"""维持低熵状态"""
results = {}
# ATP水解提供能量
atp_hydrolysis = self.atp_cycle(time_step)
results['atp_entropy'] = atp_hydrolysis
# 蛋白质折叠
protein_folding = self.protein_folding_entropy(time_step)
results['protein_entropy'] = protein_folding
# 膜电位维持
membrane_potential = self.maintain_membrane_potential(time_step)
results['membrane_entropy'] = membrane_potential
# 废物排出
waste_export = self.export_waste(time_step)
results['waste_entropy'] = waste_export
# 验证总熵增
total_internal = sum(results.values())
results['total_change'] = total_internal
return results
def atp_cycle(self, time_step: float) -> 'PhiNumber':
"""ATP循环的熵变"""
# ATP -> ADP + Pi 释放能量但增加熵
n_atp = self.atp_consumption_rate() * time_step
entropy_per_atp = PhiNumber(7.3 * 4184 / self.temperature) # kcal/mol转换
return n_atp * entropy_per_atp / self.phi
def protein_folding_entropy(self, time_step: float) -> 'PhiNumber':
"""蛋白质折叠的熵变"""
# 蛋白质折叠减少构象熵，但增加水的熵
n_proteins = self.protein_synthesis_rate() * time_step
# 蛋白质熵减
protein_entropy_decrease = PhiNumber(-50 * self.k_B * n_proteins)
# 水熵增（必须> φ * |蛋白质熵减|）
water_entropy_increase = self.phi * abs(protein_entropy_decrease.value) * 1.1
return protein_entropy_decrease + PhiNumber(water_entropy_increase)
class SelfOrganizingSystem:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
self.complexity = 1
def energy_flow_condition(self, energy_in: float,
energy_out: float,
local_entropy_rate: float,
temperature: float) -> bool:
"""检查能量流条件"""
# dE_in/dt - dE_out/dt > T * φ * dH_local/dt
net_energy_flow = energy_in - energy_out
required_flow = temperature * self.phi * abs(local_entropy_rate)
return net_energy_flow > required_flow
def information_processing_capacity(self) -> 'PhiNumber':
"""信息处理能力"""
# C_info > C_min^φ = φ^complexity
return PhiNumber(self.phi ** self.complexity)
def stability_condition(self, max_lyapunov: float,
relaxation_time: float) -> bool:
"""稳定性条件"""
# λ_max < -ln(φ)/τ_relax
critical_lyapunov = -np.log(self.phi) / relaxation_time
return max_lyapunov < critical_lyapunov
class DissipativeStructure:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def prigogine_condition(self, entropy_rate: float,
entropy_acceleration: float) -> bool:
"""Prigogine条件的φ-修正"""
# d²H/dt² < -γ_φ * (dH/dt)²
gamma_phi = 1.0 / self.phi
return entropy_acceleration < -gamma_phi * (entropy_rate ** 2)
def critical_parameter(self, system_type: str) -> 'PhiNumber':
"""临界参数（如Rayleigh数）"""
base_values = {
'convection': 1708,
'reaction_diffusion': 1,
'laser': 1
}
R_0 = base_values.get(system_type, 1)
# R_critical = R_0 * φ^(3/2)
return PhiNumber(R_0 * (self.phi ** 1.5))
def pattern_wavelength(self, system_size: float) -> 'PhiNumber':
"""图案特征波长"""
# λ = L / (n * φ)，其中n是模式数
n = int(system_size * self.phi)
return PhiNumber(system_size / (n * self.phi))
class RefrigerationSystem:
def __init__(self, T_cold: float, T_hot: float):
self.T_c = T_cold
self.T_h = T_hot
self.phi = (1 + np.sqrt(5)) / 2
def carnot_efficiency_phi(self) -> float:
"""Carnot效率的φ-修正"""
# η = 1 - T_c/T_h - ε_φ
epsilon_phi = 1 - 1/self.phi
return 1 - self.T_c/self.T_h - epsilon_phi
def minimum_work(self, heat_removed: float) -> 'PhiNumber':
"""移除热量所需的最小功"""
cop = self.T_c / (self.T_h - self.T_c)
phi_factor = self.phi # φ修正
return PhiNumber(heat_removed / (cop / phi_factor))
def approach_absolute_zero(self, n_steps: int) -> 'PhiNumber':
"""接近绝对零度"""
# T_min = T_0 * φ^(-n)
T_0 = 300 # 室温
return PhiNumber(T_0 / (self.phi ** n_steps))
class InformationStorage:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
self.l_P = 1.616e-35 # Planck长度
def maximum_density(self) -> float:
"""最大存储密度"""
# ρ_max = 1/(l_P³ * φ)
return 1 / (self.l_P ** 3 * self.phi)
def storage_lifetime(self, energy_barrier: float,
temperature: float,
error_rate: float) -> 'PhiNumber':
"""存储寿命"""
k_B = 1.38064852e-23
tau_0 = 1e-13 # 基本时间尺度
# τ = τ_0 * exp(ΔE/k_B*T) * φ^(-errors)
thermal_factor = np.exp(energy_barrier / (k_B * temperature))
error_factor = self.phi ** (-error_rate * 1e9) # 每10亿次操作的错误
return PhiNumber(tau_0 * thermal_factor * error_factor)
class Ecosystem:
def __init__(self, area: float):
self.area = area
self.phi = (1 + np.sqrt(5)) / 2
self.trophic_levels = []
def primary_production_entropy(self, solar_input: float) -> 'PhiNumber':
"""初级生产的熵变"""
# 光合作用效率约3-6%
photosynthesis_efficiency = 0.04
# 植物熵减
plant_entropy_decrease = PhiNumber(-solar_input * photosynthesis_efficiency)
# 太阳光子熵增
# 高温(6000K)到低温(300K)的熵增
photon_entropy_increase = solar_input * (1/300 - 1/6000)
return plant_entropy_decrease + PhiNumber(photon_entropy_increase)
def trophic_efficiency(self, level: int) -> float:
"""营养级效率"""
# η ≈ 0.1 ≈ φ^(-2)
return 1 / (self.phi ** 2)
def biodiversity_entropy(self, n_species: int) -> 'PhiNumber':
"""生物多样性熵"""
# Shannon熵的φ-修正
if n_species <= 1:
return PhiNumber(0)
# H = -Σ p_i * log(p_i) * φ^(-richness)
# 假设均匀分布
p = 1.0 / n_species
shannon = -n_species * p * np.log(p)
phi_factor = self.phi ** (-np.log(n_species))
return PhiNumber(shannon * phi_factor)
def verify_entropy_decrease_conditions(local_change: 'PhiNumber',
env_change: 'PhiNumber',
total_change: 'PhiNumber') -> bool:
"""验证局部熵减的所有条件"""
phi = (1 + np.sqrt(5)) / 2
# 1. 总熵必须增加
if total_change <= 0:
return False
# 2. 如果局部熵减，环境熵增必须足够大
if local_change < 0:
min_env_increase = phi * abs(local_change.value)
if env_change.value < min_env_increase:
return False
# 3. 总变化应该等于局部+环境（边界熵忽略）
if abs((local_change + env_change - total_change).value) > 1e-10:
return False
return True
def verify_life_conditions(gradient: float, temperature: float) -> bool:
"""验证生命系统的熵减条件"""
phi = (1 + np.sqrt(5)) / 2
k_B = 1.38064852e-23
# 梯度必须超过临界值
critical_gradient = k_B * temperature * phi
return gradient > critical_gradient
# 基础常数
PHI = (1 + np.sqrt(5)) / 2 # 黄金分割率
# 物理常数
K_B = 1.38064852e-23 # Boltzmann常数 (J/K)
PLANCK_LENGTH = 1.616e-35 # Planck长度 (m)
PLANCK_TIME = 5.391e-44 # Planck时间 (s)
# 熵减参数
MIN_ENTROPY_FACTOR = PHI # 最小环境熵增因子
INFORMATION_EFFICIENCY = 1/PHI # 信息处理效率上界
REVERSIBLE_COMPUTING_LIMIT = 1/PHI # 可逆计算效率极限
# 生命系统参数
ATP_ENTROPY = 7.3 * 4184 # ATP水解熵变 (J/mol)
PROTEIN_FOLDING_ENTROPY = -50 # 蛋白质折叠熵变 (k_B单位)
TROPHIC_EFFICIENCY = 0.1 # ≈ φ^(-2)
# 技术极限
CARNOT_PHI_CORRECTION = 1 - 1/PHI # ≈ 0.382
STORAGE_DENSITY_LIMIT = 1/(PLANCK_LENGTH**3 * PHI)
class EntropyDecreaseError(Exception):
"""熵减条件错误基类"""
class InsufficientGradientError(EntropyDecreaseError):
"""梯度不足错误"""
class ViolatedMinimumCostError(EntropyDecreaseError):
"""违反最小代价原理"""
class ThermodynamicViolationError(EntropyDecreaseError):
"""违反热力学定律"""