Related papers: Persistent Entropy as a Detector of Phase Transiti…
This paper presents a new robust data-driven predictive control scheme for unknown linear time-invariant systems by using input-state-output or input-output data based on whether the state is measurable. To remove the need for the…
Permutation Entropy ($PE$) is a powerful nonlinear analysis technique for univariate time series. Recently, Permutation Entropy for Graph signals ($PEG$) has been proposed to extend PE to data residing on irregular domains. However, $PEG$…
The dispersion coefficient of the constant phase element (CPE) is typically treated as an empirical fitting parameter in the analysis of impedance spectroscopy data, with no clear physical meaning. Here we seek to establish a energy-based…
The coupled entropy, $H_\kappa,$ is proven to uniquely satisfy the requirement that a generalized entropy be a measure of the uncertainty at the scale, $\sigma,$ for a class of non-exponential distributions. The coupled stretched…
We investigate the time evolution of the entropy for a paradigmatic conservative dynamical system, the standard map, for different values of its controlling parameter $a$. When the phase space is sufficiently ``chaotic'' (i.e., for large…
Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and…
We reveal the continuous phase transition in anyonic-PT symmetric systems, contrasting with the discontinuous phase transition corresponding to the discrete (anti-) PT symmetry. The continuous phase transition originates from the continuity…
We explore the behaviour of the disconnected entanglement entropy (DEE) across the topological phases of a long range interacting Kitaev chain where the long range interactions decay as a power law with an exponent $\alpha$. We show that…
This paper develops an entropy-based stability and robustness framework for nonlinear hypergraph dynamics with conservation and flow balance. We consider generator-form systems on the simplex whose state-dependent transition rates capture…
Entropy production is a universal measure of irreversibility and energy dissipation in physical, chemical, and biological systems operating far from equilibrium. However, quantifying and spatiotemporally localising it in complex processes…
We present a topological framework for analysing neural time series that integrates Transfer Entropy (TE) with directed Persistent Homology (PH) to characterize information flow in spiking neural systems. TE quantifies directional influence…
We prove that the persistence diagram of the sublevel set filtration of the quadratic form f(x) = x^T M x restricted to the unit sphere S^{n-1} is analytically determined by the eigenvalues of the symmetric matrix M. By Morse theory, the…
We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for…
The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
Complex spectra of dissipative quantum systems may exhibit degeneracies known as exceptional points (EPs). At these points the systems' dynamics may undergo drastic changes. Phenomena associated with EPs and their applications have been…
Periodically driven quantum systems can host non-equilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover $temporal$ $entanglement$ $transitions$ (TET) in a Floquet spin chain, which…
Boolean network models of strongly connected modules are capable of capturing the high regulatory complexity of many biological gene regulatory circuits. We study numerically the previously introduced basin entropy, a parameter for the…