The Shannon entropy and quantitative time irreversibility (qTIR) are statistical quantifiers that are widely used for characterizing complex processes. However, the differences and associations between them have not been subjected to detailed investigation. In this Letter, we report a comparative analysis of the Shannon entropy and qTIR using model series and real-world heartbeats. We find that the permutation-based Shannon entropy (PEn) and time irreversibility (PYs) detect nonlinearities in the model series differently according to the surrogate theory. Moreover, PEn and PYs, based on either the original or the equal-value permutation, give contradictory results for congestive heart failure cases and healthy young and elderly heartbeats. PEn quantifies the complexity by calculating the amount of mean information, whereas PYs measures the probabilistic differences among symmetric nonequilibrium distributions, and these yield different or even contradictory outcomes. Our findings demonstrate the statistical associations between the Shannon entropy and qTIR, contribute to more reliable elucidation of the nonlinear dynamics of heartbeats, and improve our understanding of the complexity and nonequilibrium nature of complex systems.The Shannon entropy and quantitative time irreversibility (qTIR) are statistical quantifiers that are widely used for characterizing complex processes. However, the differences and associations between them have not been subjected to detailed investigation. In this Letter, we report a comparative analysis of the Shannon entropy and qTIR using model series and real-world heartbeats. We find that the permutation-based Shannon entropy (PEn) and time irreversibility (PYs) detect nonlinearities in the model series differently according to the surrogate theory. Moreover, PEn and PYs, based on either the original or the equal-value permutation, give contradictory results for congestive heart failure cases and healthy young and elderly heartbeats. PEn quantifies the complexity by calculating the amount of mean information, whereas PYs measures the probabilistic differences among symmetric nonequilibrium distributions, and these yield different or even contradictory outcomes. Our findings demonstrate the statistic...

中文翻译：

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复杂系统不同甚至矛盾方面的香农熵和定量时间不可逆性

香农熵和定量时间不可逆性 (qTIR) 是广泛用于表征复杂过程的统计量词。但是，它们之间的差异和关联尚未经过详细调查。在这封信中，我们使用模型系列和真实世界的心跳报告了香农熵和 qTIR 的比较分析。我们发现基于置换的香农熵 (PEn) 和时间不可逆性 (PY) 根据代理理论以不同方式检测模型系列中的非线性。此外，PEn 和 PYs，基于原始或等值排列，对于充血性心力衰竭病例和健康的年轻人和老年人心跳给出矛盾的结果。PEn通过计算平均信息量来量化复杂度，而 PYs 测量对称非平衡分布之间的概率差异，这些会产生不同甚至相互矛盾的结果。我们的研究结果证明了香农熵和 qTIR 之间的统计关联，有助于更可靠地阐明心跳的非线性动力学，并提高我们对复杂系统的复杂性和非平衡性质的理解。香农熵和定量时间不可逆性 (qTIR) 是广泛用于表征复杂过程的统计量词。但是，它们之间的差异和关联尚未经过详细调查。在这封信中，我们使用模型系列和真实世界的心跳报告了香农熵和 qTIR 的比较分析。我们发现基于置换的香农熵 (PEn) 和时间不可逆性 (PY) 根据代理理论以不同方式检测模型系列中的非线性。此外，基于原始或等值排列的 PEn 和 PYs，对于充血性心力衰竭病例和健康的年轻人和老年人心跳给出了矛盾的结果。PEn 通过计算平均信息量来量化复杂性，而 PYs 测量对称非平衡分布之间的概率差异，这些会产生不同甚至矛盾的结果。我们的发现证明了统计... 对于充血性心力衰竭病例和健康的年轻人和老年人的心跳，给出相互矛盾的结果。PEn 通过计算平均信息量来量化复杂性，而 PYs 测量对称非平衡分布之间的概率差异，这些会产生不同甚至矛盾的结果。我们的发现证明了统计... 对于充血性心力衰竭病例和健康的年轻人和老年人的心跳，给出相互矛盾的结果。PEn 通过计算平均信息量来量化复杂性，而 PYs 测量对称非平衡分布之间的概率差异，这些会产生不同甚至矛盾的结果。我们的发现证明了统计...