class TimeDirection:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def entropy_gradient(self, state: 'SystemState') -> float:
"""计算熵梯度，确定时间方向"""
def is_forward(self, t1: float, t2: float, H1: float, H2: float) -> bool:
"""判断t1到t2是否为正向时间"""
return H2 > H1 if t2 > t1 else H1 > H2
def verify_uniqueness(self, trajectory: List[Tuple[float, float]]) -> bool:
"""验证时间方向的唯一性"""
class RecursiveUnfolding:
def __init__(self):
self.depth_history = {}
self.phi = (1 + np.sqrt(5)) / 2
def unfold(self, state: 'SystemState') -> 'SystemState':
"""递归展开操作"""
new_state = state.copy()
new_state.add_description(self.describe(state))
new_state.increment_depth()
return new_state
def is_reversible(self, state: 'SystemState') -> bool:
"""检查展开是否可逆（应该总是False）"""
unfolded = self.unfold(state)
# 尝试逆操作
return self.can_reverse(unfolded, state)
def can_reverse(self, unfolded: 'SystemState',
original: 'SystemState') -> bool:
"""尝试逆向展开"""
# 由于信息累积，这应该不可能
return False
class ZeckendorfDirectionality:
def __init__(self):
self.fib_cache = {0: 0, 1: 1, 2: 1}
def zeckendorf_representation(self, n: int) -> List[int]:
"""计算n的Zeckendorf表示"""
if n == 0:
return [0]
# 生成足够的Fibonacci数
fibs = self._generate_fibonacci_list(n)
# 贪心算法
result = []
remaining = n
for i in range(len(fibs) - 1, -1, -1):
if fibs[i] <= remaining:
result.append(1)
remaining -= fibs[i]
else:
result.append(0)
# 移除前导零
while result and result[0] == 0:
result.pop(0)
return result
def evolution_rule(self, z_n: List[int]) -> List[int]:
"""Zeckendorf表示的演化规则 n -> n+1"""
# 实现具体的演化规则
def is_evolution_reversible(self, z_n: List[int],
z_n_plus_1: List[int]) -> bool:
"""检查演化是否可逆"""
# 由于规则的不对称性，应该返回False
def verify_irreversibility(self, max_n: int = 100) -> bool:
"""验证演化的不可逆性"""
class TimeReversalOperator:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def attempt_reversal(self, state: 'SystemState') -> Optional['SystemState']:
"""尝试时间反演（应该失败）"""
# 检查是否可能构造反演状态
return None
def verify_no_reversal(self, trajectory: List['SystemState']) -> bool:
"""验证不存在时间反演"""
for i in range(len(trajectory) - 1):
if self._can_reverse_step(trajectory[i], trajectory[i+1]):
return False
return True
def _can_reverse_step(self, state1: 'SystemState',
state2: 'SystemState') -> bool:
"""检查单步是否可逆"""
# 熵增使得反演不可能
return state2.entropy() <= state1.entropy()
class IrreversibilityProof:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def prove_recursive_irreversibility(self, depth: int) -> bool:
"""证明递归展开的不可逆性"""
# 构造深度为depth的递归结构
# 证明不能反向构造
def prove_entropy_irreversibility(self, states: List['SystemState']) -> bool:
"""证明熵增的不可逆性"""
# 验证熵严格递增
for i in range(len(states) - 1):
if states[i+1].entropy() <= states[i].entropy():
return False
return True
def prove_no11_irreversibility(self, sequence: List[int]) -> bool:
"""证明no-11约束导致的不可逆性"""
# 检查约束的累积效应
class EntropyGradientField:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def gradient_at(self, state: 'SystemState') -> 'Vector':
"""计算状态空间中的熵梯度"""
def curl(self, region: 'StateSpaceRegion') -> float:
"""计算熵梯度的旋度（应该为0）"""
def verify_irrotational(self, sample_points: int = 1000) -> bool:
"""验证熵梯度场是无旋的"""
def flow_lines(self, initial: 'SystemState',
steps: int) -> List['SystemState']:
"""沿熵梯度的流线"""
class DirectionalityMeasure:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def arrow_of_time_strength(self, trajectory: List['SystemState']) -> float:
"""时间箭头的强度"""
total_entropy_increase = 0
for i in range(len(trajectory) - 1):
dH = trajectory[i+1].entropy() - trajectory[i].entropy()
total_entropy_increase += dH
return total_entropy_increase / (len(trajectory) - 1)
def reversibility_index(self, process: 'Process') -> float:
"""过程的可逆性指数（0=完全不可逆，1=完全可逆）"""
# 基于熵产生计算
def causal_asymmetry(self, state1: 'SystemState',
state2: 'SystemState') -> float:
"""因果不对称性度量"""
class CPTViolation:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def cpt_violation_amplitude(self, complexity: int) -> float:
"""CPT破坏振幅"""
return 1.0 / (self.phi ** complexity)
def measure_time_asymmetry(self, process: 'QuantumProcess') -> float:
"""测量过程的时间不对称性"""
def predict_violation(self, system: 'PhysicalSystem') -> float:
"""预测CPT破坏的大小"""
class CausalStructure:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def causal_order(self, events: List['Event']) -> List['Event']:
"""确定事件的因果顺序"""
# 基于熵增排序
def verify_no_closed_timelike_curves(self,
spacetime: 'Spacetime') -> bool:
"""验证无闭合类时曲线"""
def future_past_asymmetry(self, event: 'Event') -> float:
"""未来-过去不对称性"""
class InformationAccumulation:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def information_content(self, state: 'SystemState') -> float:
"""状态的信息含量"""
def verify_no_information_destruction(self,
process: 'Process') -> bool:
"""验证信息不灭"""
initial_info = self.information_content(process.initial_state)
final_info = self.information_content(process.final_state)
return final_info >= initial_info
def memory_direction(self, memory: 'Memory') -> str:
"""记忆的方向（应该总是指向过去）"""
return "past"
class ComputationalIrreversibility:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def landauer_limit(self, temperature: float) -> float:
"""Landauer极限"""
k_B = 1.38e-23 # Boltzmann常数
return k_B * temperature * np.log(2)
def erasure_cost(self, bits: int, temperature: float) -> float:
"""擦除信息的能量代价"""
return bits * self.landauer_limit(temperature)
def verify_computational_arrow(self,
computation: 'Computation') -> bool:
"""验证计算的时间箭头"""
class CosmologicalDirection:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def universe_entropy(self, time: float) -> float:
"""宇宙熵随时间的演化"""
# 包括物质、辐射、黑洞等贡献
def verify_no_big_crunch_reversal(self) -> bool:
"""验证即使大挤压也不能完全时间反演"""
def initial_condition_entropy(self) -> float:
"""初始条件的熵（应该很低）"""
class BlackHoleIrreversibility:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def bekenstein_hawking_entropy(self, mass: float) -> float:
"""Bekenstein-Hawking熵"""
# S = A/4 in Planck units
def formation_entropy_jump(self, initial_mass: float,
final_mass: float) -> float:
"""黑洞形成的熵跃变"""
def verify_no_white_holes(self) -> bool:
"""验证白洞不存在（时间反演的黑洞）"""
class QuantumMeasurementDirection:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def collapse_entropy_increase(self, initial_state: 'QuantumState',
measured_state: 'QuantumState') -> float:
"""波函数坍缩的熵增"""
def retrocausation_bound(self, system_size: int) -> float:
"""逆因果的上界"""
return 1.0 / (self.phi ** system_size)
class StatisticalVerification:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def boltzmann_h_theorem(self, distribution: 'Distribution') -> float:
"""Boltzmann H定理的验证"""
def fluctuation_theorem_asymmetry(self,
trajectory: 'Trajectory') -> float:
"""涨落定理的不对称性"""
class UnidirectionalSemigroup:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def compose(self, t1: 'TimeEvolution',
t2: 'TimeEvolution') -> 'TimeEvolution':
"""时间演化的复合（只能正向）"""
def has_inverse(self, t: 'TimeEvolution') -> bool:
"""检查是否有逆（应该返回False）"""
return False
def verify_semigroup_properties(self) -> bool:
"""验证半群性质"""
class EntropyPartialOrder:
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def compare(self, state1: 'SystemState',
state2: 'SystemState') -> Optional[str]:
"""比较两个状态的时间顺序"""
H1 = state1.entropy()
H2 = state2.entropy()
if H1 < H2:
return "before"
elif H1 > H2:
return "after"
else:
return None # 不可比较
def verify_partial_order_properties(self) -> bool:
"""验证偏序性质"""
# 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)
HBAR = 1.054571817e-34 # 约化Planck常数 (J·s)
C = 299792458 # 光速 (m/s)
# 方向性参数
ARROW_STRENGTH = 1.0 # 时间箭头强度
CPT_VIOLATION_SCALE = PHI ** (-10) # CPT破坏尺度
MEMORY_EFFICIENCY = 1.0 / PHI # 记忆效率因子
class DirectionalityError(Exception):
"""方向性错误基类"""
class TimeReversalError(DirectionalityError):
"""时间反演错误"""
class EntropyDecreaseError(DirectionalityError):
"""熵减少错误"""
class CausalityViolationError(DirectionalityError):
"""因果性违反错误"""