| Summary: | The complexity and the disorder of a 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noise time series are quantified by entropy of entropy (EoE) and average entropy (AE), respectively. The resulting EoE vs. AE plot of a series of 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noises of various values of <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> exhibits a distinct inverted U curve. For the 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noises, we have shown that <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> decreases monotonically as AE increases, which indicates that <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is also a measure of disorder. Furthermore, a 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noise and a cardiac interbeat (RR) interval series are considered equivalent as they have the same AE. Accordingly, we have found that the 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noises for <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> around 1.5 are equivalent to the RR interval series of healthy subjects. The pink noise at <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 1 is equivalent to atrial fibrillation (AF) RR interval series while the white noise at <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 0 is more disordered than AF RR interval series. These results, based on AE, are different from the previous ones based on spectral analysis. The testing macro-average F-score is 0.93 when classifying the RR interval series of three groups using AE-based <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, while it is 0.73 when using spectral-analysis-based <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>.
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