This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.

The sleep apnea syndrome is a chronic condition that affects the quality of life and increases the risk of severe health conditions such as cardiovascular diseases. However, the prevalence of the syndrome in the general population is considered to be heavily underestimated due to the restricted number of people seeking diagnosis, with the leading cause for this being the inconvenience of the current reference standard for apnea diagnosis: Polysomnography. To enhance patients’ awareness of the syndrome, a great endeavour is conducted in the literature. Various home-based apnea detection systems are being developed, profiting from information in a restricted set of polysomnography signals. In particular, breathing sound has been proven highly effective in detecting apneic events during sleep. The development of accurate systems requires multitudinous datasets of audio recordings and polysomnograms. In this work, we provide the first open access dataset, comprising 212 polysomnograms along with synchronized high-quality tracheal and ambient microphone recordings. We envision this dataset to be widely used for the development of home-based apnea detection techniques and frameworks.

We present a comprehensive analysis of pre-seismic anomalies as computed from the ground and space-based techniques during the recent Samos earthquake in Greece on 30 October 2020, with a magnitude M = 6.9. We proceed with a multi-parametric approach where pre-seismic irregularities are investigated in the stratosphere, ionosphere, and magnetosphere. We use the convenient methods of acoustics and electromagnetic channels of the Lithosphere–Atmosphere–Ionosphere-Coupling (LAIC) mechanism by investigating the Atmospheric Gravity Wave (AGW), magnetic field, electron density, Total Electron Content (TEC), and the energetic particle precipitation in the inner radiation belt. We incorporate two ground-based IGS GPS stations DYNG (Greece) and IZMI (Turkey) for computing the TEC and observed a significant enhancement in daily TEC variation around one week before the earthquake. For the space-based observation, we use multiple parameters as recorded from Low Earth Orbit (LEO) satellites. For the AGW, we use the SABER/TIMED satellite data and compute the potential energy of stratospheric AGW by using the atmospheric temperature profile. It is found that the maximum potential energy of such AGW is observed around six days before the earthquake. Similar AGW is also observed by the method of wavelet analysis in the fluctuation in TEC values. We observe significant energetic particle precipitation in the inner radiation belt over the earthquake epicenter due to the conventional concept of an ionospheric-magnetospheric coupling mechanism by using an NOAA satellite. We first eliminate the particle count rate (CR) due to possible geomagnetic storms and South Atlantic Anomaly (SAA) by the proper choice of magnetic field B values. After the removal of the statistical background CRs, we observe a significant enhancement of CR four and ten days before the mainshock. We use Swarm satellite outcomes to check the magnetic field and electron density profile over a region of earthquake preparation. We observe a significant enhancement in electron density one day before the earthquake. The parameters studied here show an overall pre-seismic anomaly from a duration of ten days to one day before the earthquake.

Criticality of complex systems reveals itself in various ways. One way to monitor a system at critical state is to analyze its observable manifestations using the recently introduced method of natural time. Pre-fracture electromagnetic (EM) emissions, in agreement to laboratory experiments, have been consistently detected in the MHz band prior to significant earthquakes. It has been proposed that these emissions stem from the fracture of the heterogeneous materials surrounding the strong entities (asperities) distributed along the fault, preventing the relative slipping. It has also been proposed that the fracture of heterogeneous material could be described in analogy to the critical phase transitions in statistical physics. In this work, the natural time analysis is for the first time applied to the pre-fracture MHz EM signals revealing their critical nature. Seismicity and pre-fracture EM emissions should be two sides of the same coin concerning the earthquake generation process. Therefore, we also examine the corresponding foreshock seismic activity, as another manifestation of the same complex system at critical state. We conclude that the foreshock seismicity data present criticality features as well.