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→状态空间的因果涌现
即存在着0.19比特的因果涌现，或用有效性度量得到0.595的因果涌现。
即存在着0.19比特的因果涌现，或用有效性度量得到0.595的因果涌现。
python:<syntaxhighlight lang="python3">
def calc_tpm(micro_tpm, group):
"""
Parameters
----------
micro_tpm: the transition probability matrix of system in micro level.
group: the coarse-graining methods (e.g., group = [(0, 1, 2), (3,)]: the micro states 0,1,2 are grouped into macro state 0, and the micro state 3 is grouped into macro state 1.
Returns
-------
micro_ei, macro_ei: the EI value of micro, macro TPM.
macro_tpm: the transition probability matrix of system in macro level
"""
# the number of micro/macro states
Nmi = micro_tpm.shape[0]
Nma = len(group)
# generate the mapping matrix from micro to macro
mapping = torch.zeros((Nmi, Nma), dtype=torch.float)
for j in range(Nma):
for i in group[j]:
mapping[i][j] = 1
# apply the mapping matrix to micro_tpm, and get the macro_tpm
macro_tpm = mapping.t() @ micro_tpm @ mapping
# calculate the EI of micro_tpm, macro_tpm
micro_ei = effective_information(micro_tpm)
macro_ei = effective_information(macro_tpm)
return micro_ei, macro_ei, macro_tpm
micro_tpm = torch.tensor([[1/3, 1/3, 1/3, 0], [1/3, 1/3, 1/3, 0], [1/3, 1/3, 1/3, 0], [0, 0, 0, 1]])
group = [(0, 1, 2), (3,)]
micro_ei, macro_ei, macro_tpm = calc_tpm(micro_tpm, group)
</syntaxhighlight>
== 变量角度的因果涌现 ==
== 变量角度的因果涌现 ==