Effects of ground transport on the presence of heavy metals in selected honeybee products.

Honeybees are insects very sensitive to environmental pollution and at the same time very good indicators of the pollution levels for certain types of pollutants. The morphology and ethology of these insects make them perfect vectors for dust and substances, including heavy metals produced by anthropic activities or naturally generated and deposited on foraged flora. When bees are raised to produce foods such as honey and pollen, they can easily transfer pollutants collected from contaminated flower affecting the quality of these products. However, depending on geographical location of the apiaries and their distance from pollution sources, the risk to contaminate bee products can be higher or lower requiring deep investigations. In this study, two apiaries were built near ground transport infrastructures and used as monitoring stations for investigating heavy metal presence in beehive products such as bee wax, pollen, and honey. Another apiary was placed between these two locations at a distance of 500 m from each one and used as central node to asses possible diffusion trends. Parallel, air quality was monitored in the proximity of each apiary to verify the air pollution of the environments close to these sites. The results of the study suggest that the presence of the highway and the train station affected the levels of heavy metal presence in the apiary products. Air quality near apiaries was also negatively affected by ground transport, especially in proximity of the highway. Wax resulted significantly more polluted in the apiary close to train station with elements such as Al, Zn, and Ni, while honey and pollen were significantly more polluted in the proximity of the highway with elements such as Al, Fe, Cu, and Zn. Honey was the product suffering less the contamination by heavy metals while pollen was the worse. In conclusion, the presence of transportation nodes determined a higher accumulation of heavy metals in beehive products respect the apiary placed in between, suggesting to pay particular attention in the site selection for the placement of apiaries to protect both bees and human health.

Multi-Additivity in Kaniadakis Entropy.

It is known that Kaniadakis entropy, a generalization of the Shannon-Boltzmann-Gibbs entropic form, is always super-additive for any bipartite statistically independent distributions. In this paper, we show that when imposing a suitable constraint, there exist classes of maximal entropy distributions labeled by a positive real number ℵ>0 that makes Kaniadakis entropy multi-additive, i.e., Sκ[pA∪B]=(1+ℵ)Sκ[pA]+Sκ[pB], under the composition of two statistically independent and identically distributed distributions pA∪B(x,y)=pA(x)pB(y), with reduced distributions pA(x) and pB(y) belonging to the same class.

On the Kaniadakis Distributions Applied in Statistical Physics and Natural Sciences.

Constitutive relations are fundamental and essential to characterize physical systems. By utilizing the κ-deformed functions, some constitutive relations are generalized. We here show some applications of the Kaniadakis distributions, based on the inverse hyperbolic sine function, to some topics belonging to the realm of statistical physics and natural science.

The Kinetics of Sorption-Desorption Phenomena: Local and Non-Local Kinetic Equations.

The kinetics of adsorption phenomena are investigated in terms of local and non-local kinetic equations of the Langmuir type. The sample is assumed in the shape of a slab, limited by two homogeneous planar-parallel surfaces, in such a manner that the problem can be considered one-dimensional. The local kinetic equations in time are analyzed when both saturation and non-saturation regimes are considered. These effects result from an extra dependence of the adsorption coefficient on the density of adsorbed particles, which implies the consideration of nonlinear balance equations. Non-local kinetic equations, arising from the existence of a time delay characterizing a type of reaction occurring between a bulk particle and the surface, are analyzed and show the existence of adsorption effects accompanied by temporal oscillations.

Nectar Dynamics and Pollinators Preference in Sunflower.

Nectar is a complex biochemical substance secreted with particular rhythm by flower nectaries. Nectar is the base of a mutualism in which pollinators consume nectar, as food source, and are involuntarily responsible for the transport of pollen and pollination. The dynamics and temporal patterns of nectar secretion are still not fully understood as well as the environmental and climatic factors influencing its production. The quantity and quality of nectar found in standing crops at flowering influence the mutualistic relationship with pollinators and their foraging behavior. This situation is even more significant considering the reduction in undisturbed environments, the loss of soil quality, the spread of monoculture agricultural management and the use of self-fertile hybrids. The objects of the study are understanding the relationship among soil properties and nectar quality, comparing the nectar composition in a sunflower hybrid variety and evaluate pollinator preferences in selecting nectar sources among hybrid and non-hybrid varieties. For these purposes, two different experimental tests were established. Results highlighted that fertilization strategy influenced crop biomass development, determined soil characteristics and nectar composition in Sunflower. However, when comparing nectar composition of hybrid and non-hybrid varieties of sunflower, no significant differences were found. Despite this, the analysis of number of visits on the two treatments showed statistically significant differences. This research provides further understanding of the very complex relationship among soil, crop and nectar to support the definition of agricultural management strategies and reach the optimal nectar composition level for pollinators in agricultural crops.

Boltzmann Configurational Entropy Revisited in the Framework of Generalized Statistical Mechanics.

As known, a method to introduce non-conventional statistics may be realized by modifying the number of possible combinations to put particles in a collection of single-particle states. In this paper, we assume that the weight factor of the possible configurations of a system of interacting particles can be obtained by generalizing opportunely the combinatorics, according to a certain analytical function f{π}(n) of the actual number of particles present in every energy level. Following this approach, the configurational Boltzmann entropy is revisited in a very general manner starting from a continuous deformation of the multinomial coefficients depending on a set of deformation parameters {π}. It is shown that, when f{π}(n) is related to the solutions of a simple linear difference-differential equation, the emerging entropy is a scaled version, in the occupational number representation, of the entropy of degree (κ,r) known, in the framework of the information theory, as Sharma-Taneja-Mittal entropic form.

Entropy and Non-Equilibrium Statistical Mechanics.

The present Special Issue, 'Entropy and Non-Equilibrium Statistical Mechanics', consists of seven original research papers [...].

The κ-statistics approach to epidemiology.

A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced [Formula: see text]-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of [Formula: see text]-statistics in fitting empirical data. In this paper, we use [Formula: see text]-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived [Formula: see text]-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the [Formula: see text]-Weibull model has universal features.

Equivalence between four versions of thermostatistics based on strongly pseudoadditive entropies.

The class of strongly pseudoadditive (SPA) entropies, which can be represented as an increasing continuous transformation of Shannon and Rényi entropies, have intensively been studied in previous decades. Although their mathematical structure has thoroughly been explored and established by generalized Shannon-Khinchin axioms, the analysis of their thermostatistical properties have mostly been limited to special cases which belong to two parameter Sharma-Mittal entropy class, such as Tsallis, Renyi and Gaussian entropies. In this paper we present a general analysis of the strongly pseudoadditive entropies thermostatistics by taking into account both linear and escort constraints on internal energy. We develop two types of dualities between the thermostatistics formalisms. By the first one, the formalism of Rényi entropy is transformed in the formalism of SPA entropy under general energy constraint and, by the second one, the generalized thermostatistics which corresponds to the linear constraint is transformed into the one which corresponds to the escort constraint. Thus, we establish the equivalence between four different thermostatistics formalisms based on Rényi and SPA entropies coupled with linear and escort constraints and we provide the transformation formulas. In this way we obtain a general framework which is applicable to the wide class of entropies and constraints previously discussed in the literature. As an example, we rederive maximum entropy distributions for Sharma-Mittal entropy and we establish new relationships between the corresponding thermodynamic potentials. We obtain, as special cases, previously developed expressions for maximum entropy distributions and thermodynamic quantities for Tsallis, Rényi, and Gaussian entropies. In addition, the results are applied for derivation of thermostatistical relationships for supraextensive entropy, which has not previously been considered.

Energy from Negentropy of Non-Cahotic Systems.

Negative contribution of entropy (negentropy) of a non-cahotic system, representing the potential of work, is a source of energy that can be transferred to an internal or inserted subsystem. In this case, the system loses order and its entropy increases. The subsystem increases its energy and can perform processes that otherwise would not happen, like, for instance, the nuclear fusion of inserted deuterons in liquid metal matrix, among many others. The role of positive and negative contributions of free energy and entropy are explored with their constraints. The energy available to an inserted subsystem during a transition from a non-equilibrium to the equilibrium chaotic state, when particle interaction (element of the system) is switched off, is evaluated. A few examples are given concerning some non-ideal systems and a possible application to the nuclear reaction screening problem is mentioned.

Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures.

In this paper, we present a review of recent developments on the κ -deformed statistical mechanics in the framework of the information geometry. Three different geometric structures are introduced in the κ -formalism which are obtained starting from three, not equivalent, divergence functions, corresponding to the κ -deformed version of Kullback-Leibler, "Kerridge" and Brègman divergences. The first statistical manifold derived from the κ -Kullback-Leibler divergence form an invariant geometry with a positive curvature that vanishes in the κ → 0 limit. The other two statistical manifolds are related to each other by means of a scaling transform and are both dually-flat. They have a dualistic Hessian structure endowed by a deformed Fisher metric and an affine connection that are consistent with a statistical scalar product based on the κ -escort expectation. These flat geometries admit dual potentials corresponding to the thermodynamic Massieu and entropy functions that induce a Legendre structure of κ -thermodynamics in the picture of the information geometry.

New Trends in Statistical Physics of Complex Systems.

A challenging frontier in physics concerns the study of complex and disordered systems. [...].

Cholesteric-nematic transition induced by a magnetic field in the strong-anchoring model.

We investigate the cholesteric-nematic transition induced by an external bulk field in a sample of finite thickness ℓ. The analysis is performed by considering a tilted magnetic field with respect to the easy direction imposed by rigid boundary conditions inducing planar orientation. In the case of parallel orientation between the magnetic field and of the easy direction, in the limit of ℓ→∞ we reobtain the results of de Gennes where the effective pitch of the cholesteric is a continuous function of the magnetic field diverging at the critical field related to the cholesteric-nematic transition. For finite ℓ we obtain a cascade of transitions, where the bulk expels a half-pitch at a time to avoid divergences in the elastic energy, in a similar manner as solids expel defects in the presence of strong deformation. In the case of oblique orientation between the magnetic field and the easy direction, only the completely untwisted state depends on the tilt angle. Therefore, only the cholesteric-nematic transition depends on the tilt angle while all the other magnetic transition values are unchanged.

Leptin pulsatility in formerly obese women.

Plasma leptin and growth hormone (GH) profile and pulsatility have been studied in morbidly obese subjects before and 14 months after bilio-pancreatic diversion (BPD), a bariatric technique producing massive lipid malabsorption. The maximum leptin diurnal variation (acrophase) decreased (10.27+/-1.70 vs. 22.60+/-2.79 ng x ml(-1); P=0.001), while its pulsatility index (PI) increased (1.084+/-0.005 vs. 1.050+/-0.004 ng x ml(-1) x min(-1); P=0.02) after BPD. Plasma GH acrophase increased (P=0.0001) from 0.91+/-0.20 to 4.58+/-0.80 microg x l(-1) x min(-1) after BPD as well as GH PI (1.70+/-0.13 vs. 1.20+/-0.04 microg x l(-1) x min(-1); P=0.024). Whole-body glucose uptake (M), assessed by euglycemic-hyperinsulinemic clamp, almost doubled after BPD (from 0.274+/-0.022 to 0.573+/-0.027 mmol x kgFFM(-1) x min(-1); P<0.0001), while 24 h lipid oxidation was significantly (P<0.0001) reduced (131.94+/-35.58 vs. 44.56+/-15.10 g). However, the average lipid oxidation was 97.2+/-3.1% (P<0.01) of the metabolizable lipid intake after the bariatric operation, while it was 69.2+/-8.5% before. After the operation, skeletal muscle ACC2 mRNA decreased (P<0.0001) from 452.82+/-76.35 to 182.45+/-40.69% of cyclophilin mRNA as did the malonyl-CoA (from 0.28+/-0.02 to 0.16+/-0.01 nmol x g(-1); P<0.0001). Leptin changes negatively correlated with M changes (R2=0.69, P<0.001). In a stepwise regression (R2=0.87, P=0.0055), only changes in 24 h free fatty acids (B=0.105+/-0.018, P=0.002) and glucose/insulin ratio (B=0.247+/-0.081, P=0.029) were the best predictors of leptin variations. In conclusion, the reversion of insulin resistance after BPD might allow reversal of leptin resistance, restoration of leptin pulsatility, and consequent inhibition of ACC2 mRNA expression, translating to a reduced synthesis of malonyl-CoA, which, in turn, results in increased fatty acid oxidation. Finally, since leptin inhibits GH secretion, a reduction of circulating leptin levels might have produced an increase in GH secretion, as observed in our series.

Restoration of adiponectin pulsatility in severely obese subjects after weight loss.

Diurnal variations of adiponectin levels have been studied in normal-weight men and in diabetic and nondiabetic obese subjects, but no data have been reported in obese subjects after weight loss. We collected blood samples at 1-h intervals over 24 h from seven severely obese subjects before and after massive weight loss consequent to surgical operation (bilio-pancreatic diversion [BPD]) to measure adiponectin, insulin, glucose, and cortisol levels. Insulin sensitivity was assessed by euglycemic-hyperinsulinemic clamp (M value). Studies of diurnal variations and pulsatility of adiponectin, insulin, and cortisol were performed. The pulsatility index (PI) of adiponectin increased after BPD from 0.04 to 0.11 microg/min (P = 0.01). Insulin PI significantly increased after the operation (1.50 vs. 1.08 pmol.l(-1).min(-1), P = 0.01), while cortisol PI did not significantly change. The adiponectin clearance rate changed from 0.001 +/- 10(-4).min(-1) before BPD to 0.004 +/- 8. 10(-4).min(-1) after BPD (P = 0.03). Insulin clearance increased from 0.006 +/- 6. 10(-4).min(-1) before BPD to 0.009 +/- 4.10(-4). min(-1) after BPD (P = 0.02). The M value doubled after surgery (27.08 +/- 8.5 vs. 53.34 +/- 9.3 micromol.kg(FFM)(-1).min(-1); P < 0.001) becoming similar to the values currently reported for normal-weight subjects. In conclusion, in formerly severely obese subjects, weight loss paired with the reversibility of insulin resistance restores homeostatic control of the adiponectin secretion, contributing to the reduction of cardiovascular risk already described in these patients.