Nonadditive entropy <Emphasis Type="Italic">Sq</Emphasis> and nonextensive statistical mechanics: Applications in geophysics and elsewhere

The celebrated Boltzmann-Gibbs (BG) entropy, S _BG = ?kΣ _i p _i ln p _i , and associated statistical mechanics are essentially based on hypotheses such as ergodicity, i.e., when ensemble averages coincide with time averages. This dynamical simplification occurs in classical systems (and quantum counterparts) whose microscopic evolution is governed by a positive largest Lyapunov exponent (LLE). Under such circumstances, relevant microscopic variables behave, from the probabilistic viewpoint, as (nearly) independent. Many phenomena exist, however, in natural, artificial and social systems (geophysics, astrophysics, biophysics, economics, and others) that violate ergodicity. To cover a (possibly) wide class of such systems, a generalization (nonextensive statistical mechanics) of the BG theory was proposed in 1988. This theory is based on nonadditive entropies such as \(S_q = k\frac{{1 - \sum\nolimits_i {p_i^q } }}{{q - 1}}\left( {S_1 = S_{BG} } \right)\). Here we comment some central aspects of this theory, and briefly review typical predictions, verifications and applications in geophysics and elsewhere, as illustrated through theoretical, experimental, observational, and computational results.     

EVIDENCE OF A RESPONSE-BIAS EXPLANATION OF NONEUCLIDEAN COGNITIVE MAPS*

Two groups of subjects with varying amounts of experience with the city in which they lived judged from memory distances between familiar locations. The distance judgments were processed by a multidimensional scaling algorithm (MULTISCALE) that estimates the parameters of a power function transformation of the response scale and the coordinates of the locations in k-dimensional euclidean space. The results for both subject groups suggested that inaccuracies of distance cognition do not reflect the noneuclidean nature of urban cognitive maps but are caused by response bias.     

Drought is the major limiting factor for tree-ring growth of high-altitude Canary Island pines on Tenerife

This is a detailed study of 50 wood cores sampled from 25 Canary Island pines ( Pinus canariensis ) growing in a subtropical climate close to the tree limit (at Lomo de Retamar, 2000–2100 m a.s.l.) on the southern, leeward side of Tenerife.
The Canary Island pines form tree-rings and, similarly to temperate pines, earlywood is formed during spring. But many pines fail to form tree-rings every year and one purpose for this paper has been to find a way to overcome this problem. Another purpose has been to see what correlations, if any, exist between the ring widths and meteorological data. Meteorological data have been collected since 1916 at the nearby Izaña meteorological observatory. It was also important to find the limiting factor for growth of Canary Island pines close to the tree limit.
Through cross-dating, missing rings were found to be typical for younger parts of older trees; in the same years younger trees instead had low growth. Some trees lacked more than 20 rings in a century. This study shows that it is possible to compensate for missing rings, at least when the number of missing rings is less than 10%.
Correlation studies showed that the growth of the tree rings was mainly due to the precipitation factor, particularly the annual precipitation one year before the ring formation, but also due to temperature. Strangely enough, multiple linear regression gave the highest correlation coefficient (0.50) for a combination of annual precipitation one year earlier and temperature four years earlier.     

An unusual ‘blood rain’ over the Canary Islands (Spain). The storm of January 1999

An intense storm, including strong winds, a dust storm, ‘blood rain’ and heavy rains affected the Canary Archipelago between 5 and 10 January 1999, producing damage valued at 156 million euros. The present paper analyses the weather conditions and sedimentological features of the dust. The resulting data provide a possible explanation of palaeoclimatic conditions essential for the stabilization of sand dunes in the eastern parts of the Canary Islands.     

8000 yr of black carbon accumulation in a colluvial soil from NW Spain

Analytical pyrolysis-GC/MS and solid-state ¹³C NMR (nuclear magnetic resonance) were applied to the NaOH-extractable organic matter fraction of a colluvial soil from Galicia (NW Spain) that represents more than 8500 yr of accumulation. While molecular indicators of vegetation change were looked for, it seemed likely that any such signal was disturbed by the intense fire regime of the area. This conclusion was drawn from (1) the presence of three charcoal layers, (2) the high proportion of aryl C in NMR spectra (non-quantitative) and (3) the prevalence of benzenes and polycyclic aromatic hydrocarbons (PAHs) in the chromatograms (38 ± 6% of total identified peak area), also in charcoal-poor samples. If this conclusion is accurate, the area has been subjected to burning episodes for at least 8000 yr. Additionally, the results indicate that biomass burning residues (black carbon; BC) may become NaOH extractable after long periods of degradation in mineral soil. These results add to our knowledge of the long-term fate of BC in soil, which is a potential agent in the global C cycle.     

Late Mesozoic to Paleogene stratigraphy of the Salar de Atacama Basin, Antofagasta, Northern Chile: Implications for the tectonic evolution of the Central Andes

The Salar de Atacama basin, the largest “pre-Andean” basin in Northern Chile, was formed in the early Late Cretaceous as a consequence of the tectonic closure and inversion of the Jurassic–Early Cretaceous Tarapacá back arc basin. Inversion led to uplift of the Cordillera de Domeyko (CD), a thick-skinned basement range bounded by a system of reverse faults and blind thrusts with alternating vergence along strike. The almost 6000-m-thick, upper Cretaceous to lower Paleocene sequences (Purilactis Group) infilling the Salar de Atacama basin reflects rapid local subsidence to the east of the CD. Its oldest outcropping unit (Tonel Formation) comprises more than 1000 m of continental red sandstones and evaporites, which began to accumulate as syntectonic growth strata during the initial stages of CD uplift. Tonel strata are capped by almost 3000 m of sandstones and conglomerates of western provenance, representing the sedimentary response to renewed pulses of tectonic shortening, which were deposited in alluvial fan, fluvial and eolian settings together with minor lacustrine mudstone (Purilactis Formation). These are covered by 500 m of coarse, proximal alluvial fan conglomerates (Barros Arana Formation). The top of the Purilactis Group consists of Maastrichtian-Danian alkaline lava and minor welded tuffs and red beds (Cerro Totola Formation: 70–64 Ma K/Ar) deposited during an interval of tectonic quiescence when the El Molino–Yacoraite Late Cretaceous sea covered large tracts of the nearby Altiplano-Puna domain. Limestones interbedded with the Totola volcanics indicate that this marine incursion advanced westwards to reach the eastern CD slope. CD shortening in the Late Cretaceous was accompanied by volcanism and continental sedimentation in fault bounded basins associated to strike slip along the north Chilean magmatic arc to the west of the CD domain, indicating that oblique plate convergence prevailed during the Late Cretaceous. Oblique convergence seems to have been resolved into a highly partitioned strain system where margin-parallel displacements along the thermally weakened arc coexisted with margin-orthogonal shortening associated with syntectonic sedimentation in the Salar de Atacama basin. A regionally important Early Paleocene compressional event is echoed, in the Salar de Atacama basin by a, distinctive, angular unconformity which separates Paleocene continental sediments from Purilactis Group strata. The basin also records the Eocene–Early Oligocene Incaic transpressional episode, which produced, renewed uplift in the Cordillera de Domeyko and triggered the accumulation of a thick blanket of syntectonic gravels (Loma Amarilla Formation).