A statistical complexity measure and its applications to the analysis of heart rate variability

Statistical complexity measures are proposed as general indicators of structure or correlation. Recently, R. Lopez-Ruiz introduced another measure of statistical complexity C-LMC that, like others, satisfies the boundary conditions of vanishing in the extreme ordered and disordered limits. David P. Feldman examined some properties of C-LMC and found that it is neither an intensive nor extensive thermodynamic variable, and proposed a simple alteration of C-LMC that renders its extensive. However the remedy results in a quantity that is a trivial function of the entropy density and hence of no use as a measure of structure or memory. We alter the disequilibrium term by the information of time irreversibility (information of nonlinear dynamics) and present a novel statistical complexity measure which is used to quantify the complexity caused by nonlinear dynamics. This statistical complexity measure allows reliable detection of periodic, quasi-periodic, linear stochastic and chaotic dynamics. When applied to the analysis of heart rate data, correlational structure in heart rate series is found, and the estimated statistical complexity appears to be correlated with different cardiac dynamics.