Statistical mechanics in the context of special relativity

In the present effort we show that $S_{\kappa}=-k_B \int d^3p (n^{1+\kappa}-n^{1-\kappa})/(2\kappa)$ is the unique existing entropy obtained by a continuous deformation of the Shannon-Boltzmann entropy $S_0=-k_B \int d^3p n \ln n$ and preserving unaltered its fundamental properties of concavity, additivity and extensivity. Subsequently, we explain the origin of the deformation mechanism introduced by $\kappa$ and show that this deformation emerges naturally within the Einstein special relativity. Furthermore, we extend the theory in order to treat statistical systems in a time dependent and relativistic context. Then, we show that it is possible to determine in a self consistent scheme within the special relativity the values of the free parameter $\kappa$ which results to depend on the light speed $c$ and reduces to zero as $c \to \infty$ recovering in this way the ordinary statistical mechanics and thermodynamics. The novel statistical mechanics constructed starting from the above entropy, preserves unaltered the mathematical and epistemological structure of the ordinary statistical mechanics and is suitable to describe a very large class of experimentally observed phenomena in low and high energy physics and in natural, economic and social sciences. Finally, in order to test the correctness and predictability of the theory, as working example we consider the cosmic rays spectrum, which spans 13 decades in energy and 33 decades in flux, finding a high quality agreement between our predictions and observed data. PACS number(s): 05.20.-y, 51.10.+y, 03.30.+p, 02.20.-aComment: 17 pages (two columns), 5 figures, RevTeX4, minor typing correction

Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg

It was recently published by M. Nauenberg [1] a quite long list of objections about the physical validity for thermal statistics of the theory sometimes referred to in the literature as {\it nonextensive statistical mechanics}. This generalization of Boltzmann-Gibbs (BG) statistical mechanics is based on the following expression for the entropy: S_q= k\frac{1- \sum_{i=1}^Wp_i^q}{q-1} (q \in {\cal R}; S_1=S_{BG} \equiv -k\sum_{i=1}^W p_i \ln p_i) . The author of [1] already presented orally the essence of his arguments in 1993 during a scientific meeting in Buenos Aires. I am replying now simultaneously to the just cited paper, as well as to the 1993 objections (essentially, the violation of "fundamental thermodynamic concepts", as stated in the Abstract of [1]).Comment: 7 pages including 2 figures. This is a reply to M. Nauenberg, Phys. Rev. E 67, 036114 (2003

Classical Infinite-Range-Interaction Heisenberg Ferromagnetic Model: Metastability and Sensitivity to Initial Conditions

A N-sized inertial classical Heisenberg ferromagnet, which consists in a modification of the well-known standard model, where the spins are replaced by classical rotators, is studied in the limit of infinite-range interactions. The usual canonical-ensemble mean-field solution of the inertial classical $n$-vector ferromagnet (for which $n=3$ recovers the particular Heisenberg model considered herein) is briefly reviewed, showing the well-known second-order phase transition. This Heisenberg model is studied numerically within the microcanonical ensemble, through molecular dynamics.Comment: 18 pages text, and 7 EPS figure

Nonextensivity of the cyclic Lattice Lotka Volterra model

We numerically show that the Lattice Lotka-Volterra model, when realized on a square lattice support, gives rise to a {\it finite} production, per unit time, of the nonextensive entropy $S_q= \frac{1- \sum_ip_i^q}{q-1}$ $(S_1=-\sum_i p_i \ln p_i)$. This finiteness only occurs for $q=0.5$ for the $d=2$ growth mode (growing droplet), and for $q=0$ for the $d=1$ one (growing stripe). This strong evidence of nonextensivity is consistent with the spontaneous emergence of local domains of identical particles with fractal boundaries and competing interactions. Such direct evidence is for the first time exhibited for a many-body system which, at the mean field level, is conservative.Comment: Latex, 6 pages, 5 figure

Black hole thermodynamical entropy

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy $S_{BG}$ of a $(3+1)$ black hole is proportional to its area $L^2$ ($L$ being a characteristic linear length), and not to its volume $L^3$. Similarly it exists the \emph{area law}, so named because, for a wide class of strongly quantum-entangled $d$-dimensional systems, $S_{BG}$ is proportional to $\ln L$ if $d=1$, and to $L^{d-1}$ if $d>1$, instead of being proportional to $L^d$ ($d \ge 1$). These results violate the extensivity of the thermodynamical entropy of a $d$-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is \emph{not} to be identified with the BG {\it additive} entropy but with appropriately generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ

Anomalous diffusion with absorption: Exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a non extensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion and the absorption process are discussed.Comment: RevTex, 16 pgs, 4 figures. Accepted in Physical Review

Thermostatistics of deformed bosons and fermions

Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying successive approximations. In this framework, we study the thermostatistics of q-deformed bosons and fermions and show that thermodynamics can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by the use of an appropriate Jackson derivative and q-integral. Moreover, we derive the most important thermodynamic functions and we study the q-boson and q-fermion ideal gas in the thermodynamic limit.Comment: 14 pages, 2 figure

Uso De Filtros De Carvão Ativado Granular Associado A Microrganismos Para Remoção De Fármacos No Tratamento De água De Abastecimento

The way of life of modern societies has originated the daily intake of pharmaceuticals and numerous other molecules of continuous use in aquatic environments, emerging compounds that brings potential risk for human health mainly due to exposure resulted from the inevitable contamination of sources of drinking water supply and its transference to the water treatment plants (WTP) where they are not removed. The use of granular activated carbon in filters proves to be a viable option for WTP, but satisfactory efficiency requires periodic regeneration of the material, burdening the treatment costs. However, it is noted that under low filtration rates, the natural colonization of filters by microorganisms — biofilm formation — may be an alternative for increasing the lifetime of carbon, as well as to decompose these complex molecules into assimilable mineral elements, thereby reintroducing them to the natural biogeochemical cycles. This study evaluated the activated carbon with biofilm as the filter media, during 24 weeks, under laboratory conditions, considering the removal of the pharmaceuticals diclofenac sodium, ibuprofen, naproxen and amoxicillin; experienced under batch system the potential of the microorganisms adhering to the filters in degrade the tested drugs, as well as phylogenetically identified the predominant microorganisms in biodegradation. The results show drug removal over 80%. It was observed the presence of the bacteria genus Bacillus, Burkholderia, Cupriavidus, Pseudomonas, Shinella and Sphingomonas. This study allows us to infer the capacity to remove pharmaceuticals by the bacteria present in the activated carbon filters, and the possible use of this technology as an alternative for control and removal of these substances in drinking water treatment. © 2016, ABES - Associacao Brasileira de Engenharia Sanitaria e Ambiental. All rights reserved.21470972

Glucagon-like peptide-1 receptor controls exocytosis in chromaffin cells by increasing full-fusion events

Agonists for glucagon-like-peptide-1 receptor (GLP-1R) are currently used for the treatment of type 2 diabetes and obesity. Their benefits have been centered on pancreas and hypothalamus, but their roles in other organ systems are not well understood. We studied the action of GLP-1R on secretions of adrenal medulla. Exendin-4, a synthetic analog of GLP-1, increases the synthesis and the release of catecholamines (CAs) by increasing cyclic AMP (cAMP) production, without apparent participation of cAMP-regulated guanine nucleotide exchange factor (Epac). Exendin-4, when incubated for 24 h, increases CA synthesis by promoting the activation of tyrosine hydroxylase. Short incubation (20 min) increases the quantum size of exocytotic events by switching exocytosis from partial to full fusion. Our results give a strong support to the role of GLP-1 in the fine control of exocytosis

Dance training improves cytokine secretion and viability of neutrophils in diabetic patients

Background. Evidence suggests that exercise improves neutrophil function. The decreased functional longevity of neutrophils and their increased clearance from infectious sites contribute to the increased susceptibility to infection and severity of infection observed in patients with diabetes. Objective. Herein, we investigated the effects of a dance program on neutrophil number, function, and death in type 2 diabetes mellitus (T2DM) patients and healthy volunteers. Methods. Ten patients with T2DM and twelve healthy individuals participated in a moderate-intensity dance training program for 4 months. The plasma levels of leptin, free fatty acids (FFAs), tumour necrosis factor-α (TNF-α), C-reactive protein (CRP), interleukin-1β (IL-1β), and interleukin-1 receptor antagonist (IL-1ra); neutrophil counts; extent of DNA fragmentation; cell membrane integrity; and production of TNF-α, interleukin-8 (IL-8), interleukin-6 (IL-6), and IL-1β in neutrophils were measured before and after training. Results. Training reduced plasma levels of TNF-α (1.9-fold in controls and 2.2-fold in patients with T2DM) and CRP (1.4-fold in controls and 3.4-fold in patients with T2DM). IL-1ra levels were higher in the control group (2.2-fold) after training. After training, neutrophil DNA fragmentation was decreased in patients with T2DM (90%), while the number of neutrophils increased (70% in controls and 1.1-fold in patients with T2DM). Conclusion. Dance training is a nonpharmacological strategy to reduce inflammation and improve neutrophil clearance in patients with T2DM