Phase transitions detected in complex time series by multifractal detrended fluctuation analysis

A distinctive fishtail feature in multifractal spectra derived from heart rate variability (HRV) data closely resembles similar features in plots of the Gibbs free energy versus reduced pressure for a van der Waals fluid below the critical temperature, and, in analogy to the nonideal fluid, signals a phase transition from one multifractal state to another. This fishtail feature, often overlooked or dismissed in previous studies, is observed most prevalently in unhealthy patients and suggests a realignment between multifractal variables and their thermodynamic analogs. The van der Waals analogy and subsequent alternate interpretation of multifractal variables and functions lead one to construct a three-dimensional heart health phase diagram reminiscent of a P-V-T diagram for the van der Waals fluid. The diagram which makes use of the Maxwell width as a measure of heart health produces an orderly progression from healthy to unhealthy.