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Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are…
The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…
Phase transitions in nuclei, small atomic clusters and self-gravitating systems demand the extension of thermo-statistics to ``Small'' systems. The main obstacle is the thermodynamic limit. It is shown how the original definition of the…
A commonly-used paradigm to estimate changes in the frequency of past events or the size of populations is to consider the occurrence rate of archaeological/environmental samples found at a site over time. The reliability of such a…
We map the mean-field Ising model equation of state onto the QCD phase diagram, and reconstruct the full coexistence region in the case of a first order phase transition. Beyond the coexistence line, we maintain access to the spinodal…
The annual temperature cycle of the earth closely follows the annual cycle of solar flux. At temperate latitudes, both driving and response cycles are well described by a strong annual sinusoidal component and a non-vanishing semiannual…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
The ocean is filled with phytoplankton that contribute as much photosynthesis as all land plants combined, making them vital to the carbon cycle and climate system. Recent advances in flow cytometry allow oceanographers to measure the…
This paper studies stochastic convergence of per capita CO$_2$ emissions in 28 OECD countries for the 1901-2009 period. The analysis is carried out at two aggregation levels, first for the whole set of countries (joint analysis) and then…
Anticipating critical transitions in the Earth system is of great societal relevance, yet there may be intrinsic limitations to their predictability. For instance, from the theory of dynamical systems possessing multiple chaotic attractors,…
A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site but also the direction of the bond between them using both analytical and numerical methods. The phase diagram…
Recent findings suggest that abnormal operating conditions of equipment in the oil and gas supply chain represent a large fraction of anthropogenic methane emissions. Thus, effective mitigation of emissions necessitates rapid identification…
We present a statistical method for detecting and analysing state changes in experimental measurements using the Cuscore statistic and its special case, the Centred Cuscore statistic. These statistics are designed to identify deviations in…
How strong are quantitative contributions of the key natural modes of climate variability and the anthropogenic factor characterized by the changes of the radiative forcing of greenhouse gases in the atmosphere to the trends of the surface…
Difference of degeneracy of the low-spin (LS) and high-spin (HS) states causes interesting entropy effects on spin-crossover phase transitions and charge transfer phase transitions in materials composed of the spin-crossover atoms.…
This study investigates how visibility graphs constructed from Monte Carlo Markov Chain time series of spin models capture the critical behavior of the system. More precisely, we show that this approach identifies continuous phase…
The Berezinskii-Kosterlitz-Thouless (BKT) transitions of the six-state clock model on the square lattice are investigated by means of the corner-transfer matrix renormalization group method. The classical analogue of the entanglement…
The Ghil-Sellers energy balance model of Earth's climate, features -- for a considerable range of the solar intensity -- two stable climate states (a warm and a cold snowball Earth), where the bistability results from the celebrated…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
During most of the Phanerozoic eon, which began about a half-billion years ago, there were few glacial intervals until the late Pliocene 2.75 million years ago. Beginning at that time, the Earth's climate entered a period of instability…