A novel parameter for nonequilibrium analysis in reconstructed state spaces

Abstract

Kernel methods are widely used for probability estimation by measuring the distribution of low-passed vector distances in reconstructed state spaces. However, the information conveyed by the vector distances that are greater than the threshold has received little attention. In this paper, we consider the probabilistic difference of the kernel transformation in reconstructed state spaces, and derive a novel nonequilibrium descriptor by measuring the fluctuations of the vector distance with respect to the tolerance. We verify the effectiveness of the proposed kernel probabilistic difference using three chaotic series (logistic, Henon, and Lorenz) and a first-order autoregressive series according to the surrogate theory, and we use the kernel parameter to analyze real-world heartbeat data. In the heartbeat analysis, the kernel probabilistic difference, particularly that based on the Kullback--Leibler divergence, effectively characterizes the physiological complexity loss related to reduced cardiac dynamics in the elderly and diseased heartbeat data. Overall, the kernel probabilistic difference provides a novel method for the quantification of nonequilibria by characterizing the fluctuation theorem in reconstructed state spaces, and enables reliable detection of cardiac physiological and pathological information from heart rates.

arXiv comment13 pages, 5 figures

References in corpus (17)

• Measuring Information Transfer
• Improved surrogate data for nonlinearity tests
• Surrogate time series
• Multifractality in Human Heartbeat Dynamics
• Complex network approaches to nonlinear time series analysis
• Kernel method for nonlinear Granger causality
• Fluctuation Theorems
• Estimating dissipation from single stationary trajectories
• Fluctuation theorem uncertainty relation
• Kernel Granger causality and the analysis of dynamical networks
• Experimental determination of irreversible entropy production in out-of-equilibrium mesoscopic quantum systems
• Quantifying time irreversibility using probabilistic differences between symmetric permutations
• Equal heartbeat intervals and their effects on the nonlinearity of permutation-based time irreversibility in heart rate
• Permutation entropy revisited
• Complexity Analysis of Chaos and Other Fluctuating Phenomena
• Time irreversibility and amplitude irreversibility measures for nonequilibrium processes
• Focus on some Nonequilibrium Issues