Alpha 1-acid glycoprotein is upregulated in severe COVID-19 patients and decreases neutrophil NETs in SARS-CoV-2 infection.

Orosomucoid, or alpha-1 acid glycoprotein (AGP), is a major acute-phase protein expressed in response to systemic injury and inflammation. AGP has been described as an inhibitor of neutrophil migration on sepsis, particularly its immunomodulation effects. AGP's biological functions in coronavirus disease 2019 (COVID-19) are not understood. We sought to investigate the role of AGP in severe COVID-19 infection patients and neutrophils infected with severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). Epidemiological data, AGP levels, and other laboratory parameters were measured in blood samples from 56 subjects hospitalized in the ICU with SARS-CoV-2 infection. To evaluate the role of AGP in NETosis in neutrophils, blood samples from health patients were collected, and neutrophils were separated and infected with SARS-CoV-2. Those neutrophils were treated with AGP or vehicle, and NETosis was analyzed by flow cytometry. AGP was upregulated in severe COVID-19 patients (p<0.05). AGP level was positively correlated with IL-6 and C-reactive protein (respectively, p=0.005, p=0.002) and negatively correlated with lactate (p=0.004). AGP treatment downregulated early and late NETosis (respectively, 35.7% and 43.5%) in neutrophils infected with SARS-CoV-2 and up-regulated IL-6 supernatant culture expression (p<0.0001). Our data showed increased AGP in COVID-19 infection and contributed to NETosis regulation and increased IL-6 production, possibly related to the Cytokine storm in COVID-19.

Prospective Assessment of a Protocol Using Neuromonitoring, Early Limb Reperfusion, and Selective Temporary Aneurysm Sac Perfusion to Prevent Spinal Cord Injury During Fenestrated-branched Endovascular Aortic Repair.

OBJECTIVE: The aim of this study was to analyze the outcomes of a standardized protocol using routine CSFD, neuromonitoring, LL reperfusion, and selective TASP to prevent SCI during F-BEVAR. BACKGROUND: SCI is to be the most devastating complication for the patient, family, and surgeon, with impact on patient's quality of life and long-term prognosis. An optimal standardized protocol may be used to improve outcomes. METHODS: Patients enrolled in a prospective, nonrandomized single-center study between 2013 and 2018. A SCI prevention protocol was used for TAAAS or complex abdominal aneurysms with ≥5-cm supraceliac coverage including CSFD, neuromonitoring, LL reperfusion, and selective TASP. Endpoints included mortality and rates of SCI. RESULTS: SCI prevention protocol was used in 170 of 232 patients (73%) treated by F-BEVAR. Ninety-one patients (55%) had changes in neuromonitoring, which improved with maneuvers in all except for 9 patients (10%) who had TASP. There was one 30-day or in-hospital mortality (0.4%). Ten patients (4%) developed SCIs including in 1% (1/79) of patients with normal neuromonitoring and 10% (9/91) of those who had decline in neuromonitoring ( P = 0.02). Permanent paraplegia occurred in 2 patients (1%). Factors associated with SCI included total operating time (odds ratio 1.5, 95% confidence interval 1.1-2.2, P = 0.02) and persistent changes in neuromonitoring requiring TASP (odds ratio 15.7, 95% confidence interval 2.9-86.2, P = 0.001). CONCLUSION: This prospective nonrandomized study using a standardized strategy to prevent SCI was associated with low incidence of the SCI during F-BEVAR. Permanent paraplegia occurred in 1%.

Impact of aortic wall thrombus on late changes in renal function among patients treated by fenestrated-branched endografts.

OBJECTIVE: Renal function deterioration is an important determinant of mortality in patients treated for complex aortic aneurysms. We have previously determined that catheter and guidewire manipulation in diseased aortas during fenestrated-branched endovascular aneurysm repair (F-BEVAR) is associated with risk of renal function deterioration. The aim of this study was to describe the impact of atherothrombotic aortic wall thrombus (AWT) on renal function deterioration among patients treated by F-BEVAR for pararenal and extent IV thoracoabdominal aortic aneurysms. METHODS: Clinical data of 212 patients treated for complex aortic aneurysms with F-BEVAR were entered into a prospectively maintained database (2007-2015). AWT was evaluated by computed tomography angiography using volumetric measurements in nonaneurysmal aortic segments. AWT was classified as mild, moderate, or severe using objective assessment of the number of affected segments, thrombus type, thickness, area, and circumference. Acute kidney injury (AKI) was defined using Risk, Injury, Failure, Loss of kidney function, and End-stage renal disease (RIFLE) criteria, and renal function deterioration was defined by a decline in estimated glomerular filtration rate (eGFR) >30% from baseline. Patient survival and renal outcomes were assessed at dismissal, at 6 to 8 weeks, at 6 months, and annually, including AKI, serum creatinine concentration, eGFR, chronic kidney disease stage, need for renal replacement therapy, and presence of kidney infarction. RESULTS: There were 169 male (80%) and 43 female (20%) patients with a mean age of 75 ± 7 years. Aneurysm extent was pararenal in 157 patients and extent IV thoracoabdominal aortic aneurysm in 55 patients. A total of 700 renal-mesenteric arteries were incorporated (3.1 ± 1 vessels/patient). AWT was classified as mild in 98 patients (46%), moderate in 75 (35%), and severe in 39 (19%). At 30 days, 45 patients (21%) developed AKI. Decline in eGFR and kidney infarction were associated with higher AWT volume index and severe AWT classification (P < .05). There was no association of AWT with 30-day mortality, which was 0.5% for the entire cohort. Mean follow-up was 29 ± 23 months. Freedom from renal function deterioration was 73% ± 6% for mild, 81% ± 6% for moderate, and 66% ± 8% for severe AWT patients at 3 years (P = .012) and 46% ± 9% and 82% ± 4% for those with or without AKI after the initial procedure (P < .001). Overall, 41 patients (19%) had progression of chronic kidney disease stage, but none of the patients required renal replacement therapy. Survival was 73% ± 5% for mild, 72% ± 6% for moderate, and 69% ± 10% for severe AWT patients at 3 years (P = .67). CONCLUSIONS: AWT is a significant predictor of AKI and continued decline in renal function after the initial F-BEVAR procedure. Longer follow-up time is needed to determine the actual impact of AWT on survival.

Evolution from physician-modified to company-manufactured fenestrated-branched endografts to treat pararenal and thoracoabdominal aortic aneurysms.

OBJECTIVE: The purpose of this study was to review treatment trends and outcomes of patients who underwent fenestrated-branched endovascular aneurysm repair (F-BEVAR) of pararenal aneurysms (PRAs) or thoracoabdominal aortic aneurysms (TAAAs) using physician-modified endografts (PMEGs) or company-manufactured devices (CMDs). METHODS: We reviewed the clinical data of 316 consecutive patients (242 male patients; mean age, 75 ± 8 years) who underwent F-BEVAR between 2007 and 2016. F-BEVAR was performed under two prospective investigational device exemption protocols since 2013. End points were mortality, major adverse events (MAEs), patient survival, reintervention, branch instability, aneurysm-related mortality, renal function deterioration, and target vessel patency. RESULTS: There were 145 patients (46%) treated by PMEGs (84 PRAs, 26 extent IV and 35 extent I-III TAAAs) and 171 patients (54%) who had CMDs (88 PRAs, 42 extent IV and 41 extent I-III TAAAs). Choice of endograft evolved from PMEGs in 131 patients (83%) treated in the first half of experience to CMDs in 144 patients (91%) treated in the second half of experience (P < .001). Patients treated by PMEGs had significantly (P < .05) larger aneurysms, more chronic pulmonary and kidney disease, and higher comorbidity severity scores. A total of 1081 renal-mesenteric arteries were targeted in both groups. Technical success was lower for PMEGs (98% vs 99.5%; P = .02). Thirty-day mortality was 5.5% for PMEGs (PRAs, 1.2%; extent IV 3.8% and extent I-III, 17.1%) and 0% for CMDs (P = .0018). Patients treated by PMEGs had significantly more (P < .001) MAEs (48% vs 23%) and longer hospital stay (9 ± 10 days vs 6 ± 6 days; P = .001). Mean follow-up was significantly longer for patients treated by PMEGs (38 ± 26 months vs 14 ± 12 months; P < .001). At 3 years, patient survival (68% ± 4% vs 67% ± 8%; P = .11), freedom from reintervention (68% ± 4% vs 68% ± 8%; P = .17), primary (94% ± 2% vs 92% ± 2%; P = .64) and secondary target vessel patency (98% ± 1% vs 98% ± 1%; P = .89), and freedom from renal function deterioration (75% ± 4% vs 65% ± 6%; P = .24) were similar for patients treated by PMEGs or CMDs, respectively. CONCLUSIONS: Choice of F-BEVAR evolved from PMEGs to almost exclusively CMDs under physician-sponsored investigational device exemption protocols. PMEG patients had more comorbidities and larger aneurysms. CMDs were performed with higher technical success, no mortality, and fewer MAEs.

Characterization of the kallikrein-kinin system, metalloproteinases, and their tissue inhibitors in the in-stent restenosis after peripheral percutaneous angioplasty.

BACKGROUND: The kallikrein-kinin system (KKS) has several direct and indirect effects on cells and cellular mediators involved in the inflammatory process. Studies about inflammation on percutaneous transluminal angioplasty with stent (PTA/stent) to treat peripheral arterial disease (PAD) in humans are scarce. The matrix metalloproteinases (MMPs) are calcium-dependent zinc-containing endopeptidases expressed in various cells and tissues such as fibroblasts, inflammatory cells, and, smooth muscle cells. Changes in the extracellular matrix (ECM) take place in the pathogenesis of many cardiovascular pathologies. MMPs and their inhibitors (tissue inhibitors of metalloproteinases [TIMPs]) are crucial in ECM remodeling in both physiologic and pathologic conditions. The aim of this study was to evaluate the role of the KKS and the MMP metabolism, which are important mediators that may contribute to tissue repair, in the process of arterial restenosis due to intimal hyperplasia in the femoropopliteal segment with the aim of developing new interventions. METHODS: Thirty-nine consecutive patients were selected (regardless of ethnic group, age, or sex) for revascularization, who underwent PTA/stent of the femoropopliteal segment. Twenty-five patients with the same clinical characteristics who were scheduled for diagnostic angiography but not subjected to PTA/nitinol stent were also selected. The concentrations in blood of total and kininogen fractions were evaluated using immunoenzymatic methods. Plasma kallikrein was evaluated by the colorimetric method. Tissue kallikrein was evaluated by the spectrophotometric method. The activity of kininase II was measured by fluorometric analysis. Quantification of MMPs was performed by zymography, which is an electrophoresis technique, and TIMPs were measured by enzyme-linked immunosorbent assay. RESULTS: Among the 31 patients who completed the survey, there were 10 cases of angiographically defined restenosis of >50%, and 21 cases without restenosis. There was an increase in the concentrations of the substrates (high-molecular-weight kininogens and lower molecular weight kininogens) and enzymes (plasma and tissue kallikrein) in patients with restenosis, indicating activation of this inflammatory pathway in these patients. The activity of kininase II was not significantly different between the groups of patients studied. There were no statistical differences between restenosis and no restenosis patients for both MMPs and TIMPs dosage, but there is an upward trend of MMPs in time 6 months in patients with restenosis. CONCLUSIONS: With the aim of identifying factors contributing to restenosis after endovascular intervention, this study showed evidence of high activation of the KKS in the pathologic inflammatory process of PTA/stent restenosis. In the other hand, it could not show participation of metalloproteinase metabolism in PTA/stent restenosis.

MMP-2 and MMP-9 levels in plasma are altered and associated with mortality in COVID-19 patients.

Respiratory symptoms are one of COVID-19 manifestations, and the metalloproteinases (MMPs) have essential roles in the lung physiology. We sought to characterize the plasmatic levels of matrix metalloproteinase-2 and 9 (MMP-2 and MMP-9) in patients with severe COVID-19 and to investigate an association between plasma MMP-2 and MMP-9 levels and clinical outcomes and mortality. MMP-2 and MMP-9 levels in plasma from patients with COVID-19 treated in the ICU (COVID-19 group) and Control patients were measured with the zymography. The study groups were matched for age, sex, hypertension, diabetes, BMI, and obesity profile. MMP-2 levels were lower and MMP-9 levels were higher in a COVID-19 group (p < 0.0001) compared to Controls. MMP-9 levels in COVID-19 patients were not affected by comorbidity such as hypertension or obesity. MMP-2 levels were affected by hypertension (p < 0.05), but unaffected by obesity status. Notably, hypertensive COVID-19 patients had higher MMP-2 levels compared to the non-hypertensive COVID-19 group, albeit still lower than Controls (p < 0.05). No association between MMP-2 and MMP-9 plasmatic levels and corticosteroid treatment or acute kidney injury was found in COVID-19 patients. The survival analysis showed that COVID-19 mortality was associated with increased MMP-2 and MMP-9 levels. Age, hypertension, BMI, and MMP-2 and MMP-9 were better predictors of mortality during hospitalization than SAPS3 and SOFA scores at hospital admission. In conclusion, a significant association between MMP-2 and MMP-9 levels and COVID-19 was found. Notably, MMP-2 and MMP-9 levels predicted the risk of in-hospital death suggesting possible pathophysiologic and prognostic roles.

Preloaded Catheters and Guide-Wire Systems to Facilitate Catheterization During Fenestrated and Branched Endovascular Aortic Repair.

OBJECTIVE: The aim of this study was to review the clinical outcomes for patients treated for pararenal (PRA) and thoracoabdominal aortic aneurysms (TAAAs) by fenestrated-branched endovascular aortic repair (F-BEVAR) using preloaded systems (PLS). METHODS: We reviewed clinical data of 83 patients (64 male, mean age 75 ± 7 years) enrolled in a prospective study to investigate F-BEVAR. All patients had PLS, which included two catheters or two through-and-through guide wires with 12-Fr trans-brachial sheaths positioned in the descending thoracic aorta. Outcome measurements were technical success defined as successful deployment of the main fenestrated stent graft and cannulation of all target vessels, total endovascular time, total lower extremity ischemia time and complications, 30-day mortality, and major adverse events (MAEs). RESULTS: Aneurysm extent was PRA in 27 patients and TAAA in 56 (35 extent IV and 21 extent I-III). A total of 333 target vessels were incorporated with an average of 4 ± 0.4 vessels per patient. Technical success was 99.7%. Total endovascular time was 160 ± 51 min. Sixty-five (78%) patients had motor and somatosensory evoked potentials monitoring, and lower extremity ischemia time was 115 ± 42 min. There were no 30-day mortalities. Fifteen patients (18%) had MAEs, including three (3.6%) minor ischemic strokes. There were no upper extremity complications. All ischemic strokes occurred in female patients (3.6% vs. 0%, P = .001). One (1.2%) patient had paraplegia. CONCLUSION: This study shows high technical success and early lower limb reperfusion using PLS with trans-brachial access. The risk of stroke, especially in female patients, should be carefully assessed by review of preoperative arch imaging.

Planning endovascular aortic repair with standard and fenestrated-branched endografts.

Endovascular aortic repair (EVAR) has been accepted as the first treatment option in most patients with infrarenal and thoracic aortic aneurysms. Advantages include its minimal invasive approach and lower risk of mortality and morbidity compared to open surgical repair. In patients with complex aneurysms involving side branches, novel techniques of parallel, fenestrated and branched endografts have expanded the indications of EVAR. Preoperative planning is of paramount importance to achieve technical success and to minimize risks of these procedures. In most centers, anatomical measurements are based on helical computed tomography angiography and/or magnetic resonance angiography. This article summarizes the most important aspects on planning standard and complex EVAR to treat aortic aneurysms and dissections.

Elastase-2, an angiotensin II-generating enzyme, contributes to increased angiotensin II in resistance arteries of mice with myocardial infarction.

BACKGROUND AND PURPOSE: Angiotensin II (Ang II), whose generation largely depends on angiotensin-converting enzyme (ACE) activity, mediates most of the renin-angiotensin-system (RAS) effects. Elastase-2 (ELA-2), a chymotrypsin-serine protease elastase family member 2A, alternatively generates Ang II in rat arteries. Myocardial infarction (MI) leads to intense RAS activation, but mechanisms involved in Ang II-generation in resistance arteries are unknown. We hypothesized that ELA-2 contributes to vascular Ang II generation and cardiac damage in mice subjected to MI. EXPERIMENTAL APPROACH: Concentration-effect curves to Ang I and Ang II were performed in mesenteric resistance arteries from male wild type (WT) and ELA-2 knockout (ELA-2KO) mice subjected to left anterior descending coronary artery ligation (MI). KEY RESULTS: MI size was similar in WT and ELA-2KO mice. Ejection fraction and fractional shortening after MI similarly decreased in both strains. However, MI decreased stroke volume and cardiac output in WT, but not in ELA-2KO mice. Ang I-induced contractions increased in WT mice subjected to MI (MI-WT) compared with sham-WT mice. No differences were observed in Ang I reactivity between arteries from ELA-2KO and ELA-2KO subjected to MI (MI-ELA-2KO). Ang I contractions increased in arteries from MI-WT versus MI-ELA-2KO mice. Chymostatin attenuated Ang I-induced vascular contractions in WT mice, but did not affect Ang I responses in ELA-2KO arteries. CONCLUSIONS AND IMPLICATIONS: These results provide the first evidence that ELA-2 contributes to increased Ang II formation in resistance arteries and modulates cardiac function after MI, implicating ELA-2 as a key player in ACE-independent dysregulation of the RAS.

Elastase-2, a Tissue Alternative Pathway for Angiotensin II Generation, Plays a Role in Circulatory Sympathovagal Balance in Mice.

In vitro and ex vivo experiments indicate that elastase-2 (ELA-2), a chymotrypsin-serine protease elastase family member 2A, is an alternative pathway for angiotensin II (Ang II) generation. However, the role played by ELA-2 in vivo is unclear. We examined ELA-2 knockout (ELA-2KO) mice compared to wild-type (WT) mice and determined whether ELA-2 played a role in hemodynamics [arterial pressure (AP) and heart rate (HR)], cardiocirculatory sympathovagal balance and baroreflex sensitivity. The variability of systolic arterial pressure (SAP) and pulse interval (PI) for evaluating autonomic modulation was examined for time and frequency domains (spectral analysis), whereas a symbolic analysis was also used to evaluate PI variability. In addition, baroreflex sensitivity was examined using the sequence method. Cardiac function was evaluated echocardiographically under anesthesia. The AP was normal whereas the HR was reduced in ELA-2KO mice (425 ± 17 vs. 512 ± 13 bpm from WT). SAP variability and baroreflex sensitivity were similar in both strains. The LF power from the PI spectrum (33.6 ± 5 vs. 51.8 ± 4.8 nu from WT) and the LF/HF ratio (0.60 ± 0.1 vs. 1.45 ± 0.3 from WT) were reduced, whereas the HF power was increased (66.4 ± 5 vs. 48.2 ± 4.8 nu from WT) in ELA-2KO mice, indicating a shift toward parasympathetic modulation of HR. Echocardiographic examination showed normal fractional shortening and an ejection fraction in ELA-2KO mice; however, the cardiac output, stroke volume, and ventricular size were reduced. These findings provide the first evidence that ELA-2 acts on the sympathovagal balance of the heart, as expressed by the reduced sympathetic modulation of HR in ELA-2KO mice.

Repulsive particles under a general external potential: Thermodynamics by neglecting thermal noise.

A recent proposal of an effective temperature θ, conjugated to a generalized entropy s_{q}, typical of nonextensive statistical mechanics, has led to a consistent thermodynamic framework in the case q=2. The proposal was explored for repulsively interacting vortices, currently used for modeling type-II superconductors. In these systems, the variable θ presents values much higher than those of typical room temperatures T, so that the thermal noise can be neglected (T/θ≃0). The whole procedure was developed for an equilibrium state obtained after a sufficiently long-time evolution, associated with a nonlinear Fokker-Planck equation and approached due to a confining external harmonic potential, ϕ(x)=αx^{2}/2 (α>0). Herein, the thermodynamic framework is extended to a quite general confining potential, namely ϕ(x)=α|x|^{z}/z (z>1). It is shown that the main results of the previous analyses hold for any z>1: (i) The definition of the effective temperature θ conjugated to the entropy s_{2}. (ii) The construction of a Carnot cycle, whose efficiency is shown to be η=1-(θ_{2}/θ_{1}), where θ_{1} and θ_{2} are the effective temperatures associated with two isothermal transformations, with θ_{1}>θ_{2}. The special character of the Carnot cycle is indicated by analyzing another cycle that presents an efficiency depending on z. (iii) Applying Legendre transformations for a distinct pair of variables, different thermodynamic potentials are obtained, and furthermore, Maxwell relations and response functions are derived. The present approach shows a consistent thermodynamic framework, suggesting that these results should hold for a general confining potential ϕ(x), increasing the possibility of experimental verifications.

Off-the-shelf fenestrated and branched stent graft designs for abdominal aortic aneurysm repair.

Endovascular repair of pararenal and thoracoabdominal aortic aneurysms with fenestrated and branched stent grafts has been increasingly utilized with high technical success and low morbidity and mortality. Freedom from branch-related events has been reported at 89% in 5 years, including any branch-related endoleak, stenosis, kink, disconnection, or occlusion. Patient-specific stent grafts have the advantage of fitting patients' anatomy, but require a 6- to 8-week period for customization. Off-the-shelf stent grafts have been developed based on a relative predictability of renal-mesenteric vessels. Advantages of an off-the-shelf design are elimination of treatment delays and standardization of manufacturing, planning, and implantation techniques. Nevertheless, these devices have significant anatomic constraints that limit their application to all patients. In addition, it is critical that long-term durability of branches either matches or surpasses what has already been reported for patient-specific designs. This article summarizes the state of the art for off-the-shelf fenestrated and branched stent grafts, with emphasis in anatomic feasibility, limitations, and preliminary clinical results.

Energy performance and greenhouse gas emissions of kelp cultivation for biogas and fertilizer recovery in Sweden.

The cultivation of seaweed as a feedstock for third generation biofuels is gathering interest in Europe, however, many questions remain unanswered in practise, notably regarding scales of operation, energy returns on investment (EROI) and greenhouse gas (GHG) emissions, all of which are crucial to determine commercial viability. This study performed an energy and GHG emissions analysis, using EROI and GHG savings potential respectively, as indicators of commercial viability for two systems: the Swedish Seafarm project's seaweed cultivation (0.5ha), biogas and fertilizer biorefinery, and an estimation of the same system scaled up and adjusted to a cultivation of 10ha. Based on a conservative estimate of biogas yield, neither the 0.5ha case nor the up-scaled 10ha estimates met the (commercial viability) target EROI of 3, nor the European Union Renewable Energy Directive GHG savings target of 60% for biofuels, however the potential for commercial viability was substantially improved by scaling up operations: GHG emissions and energy demand, per unit of biogas, was almost halved by scaling operations up by a factor of twenty, thereby approaching the EROI and GHG savings targets set, under beneficial biogas production conditions. Further analysis identified processes whose optimisations would have a large impact on energy use and emissions (such as anaerobic digestion) as well as others embodying potential for further economies of scale (such as harvesting), both of which would be of interest for future developments of kelp to biogas and fertilizer biorefineries.

Second law and entropy production in a nonextensive system.

A model of superconducting vortices under overdamped motion is currently used for describing type-II superconductors. Recently, this model has been identified to a nonlinear Fokker-Planck equation and associated to an entropic form characteristic of nonextensive statistical mechanics, S(2)(t)≡S((q)=2)(t). In the present work, we consider a system of superconducting vortices under overdamped motion, following an irreversible process, so that by using the corresponding nonlinear Fokker-Planck equation, the entropy time rate [dS(2)(t)/dt] is investigated. Both entropy production and entropy flux from the system to its surroundings are analyzed. Molecular dynamics simulations are carried for this process, showing a good agreement between the numerical and analytical results. It is shown that the second law holds within the present framework, and we exhibit the increase of S(2)(t) with time, up to its stationary-state value.

Probability distributions and associated nonlinear Fokker-Planck equation for the two-index entropic form S(q,δ).

The probability distributions and associated Fokker-Planck equation of the recently postulated entropic form, S(q,δ), are investigated. This entropy was proposed as an unification of the well-known S(q) of nonextensive-statistical mechanics and S(δ), which appeared lately as a possibly appropriate candidate for the black-hole entropy. The connection between S(q,δ) and a nonlinear Fokker-Planck equation, such as to satisfy an H-theorem, is explored. The stationary-state probability distribution follows a transcendental equation, which is solved numerically for typical values of q and δ. The same transcendental equation is obtained through the maximum-entropy principle, showing that the two procedures are equivalent.

Comment on "Vortex distribution in a confining potential".

A system of interacting vortices is considered as an appropriate model for describing properties of type-II superconductors, and it has been shown lately to be deeply associated with nonextensive statistical mechanics. Herein we comment on a recent investigation of this model [M. Girotto, A. P. dos Santos, and Y. Levin, Phys. Rev. E 88, 032118 (2013)], which tried to contradict this assertion, based on a mean-field type of solution, compared with numerical-simulation data that correspond typically to a regime characterized by low concentrations of particles, as well as very high temperatures. It is shown that the physical situations analyzed differ significantly from those of a real superconducting phase. The analytical solution obtained from such a mean-field approximation shows a discrepancy with respect to the results of molecular-dynamics numerical simulations, which increases as the temperature is lowered towards the superconducting phase, as expected. We demonstrate that these results, when interpreted properly by means of an analytical solution within the framework of nonextensive statistical mechanics, present a remarkable agreement between molecular-dynamics simulations and theoretical results, for all temperatures, specially for those temperatures associated with the existence of type-II superconductivity.

Probability distributions extremizing the nonadditive entropy S(δ) and stationary states of the corresponding nonlinear Fokker-Planck equation.

Under the assumption that the physically appropriate entropy of generic complex systems satisfies thermodynamic extensivity, we investigate the recently introduced entropy S(δ) (which recovers the usual Boltzmann-Gibbs form for δ=1) and establish the microcanonical and canonical extremizing distributions. Using a generalized version of the H theorem, we find the nonlinear Fokker-Planck equation associated with that entropic functional and calculate the stationary-state probability distributions. We demonstrate that both approaches yield one and the same equation, which in turn uniquely determines the probability distribution. We show that the equilibrium distributions asymptotically behave like stretched exponentials, and that, in appropriate probability-energy variables, an interesting return occurs at δ=4/3. As a mathematically simple illustration, we consider the one-dimensional harmonic oscillator and calculate the generalized chemical potential for different values of δ.

Time evolution of interacting vortices under overdamped motion.

A system of interacting vortices under overdamped motion, which has been commonly used in the literature to model flux-front penetration in disordered type-II superconductors, was recently related to a nonlinear Fokker-Planck equation, characteristic of nonextensive statistical mechanics, through an analysis of its stationary state. Herein, this connection is extended by means of a thorough analysis of the time evolution of this system. Numerical data from molecular-dynamics simulations are presented for both position and velocity probability distributions P(x,t) and P(v(x),t), respectively; both distributions are well fitted by similar q-Gaussian distributions, with the same index q=0, for all times considered. Particularly, the evolution of the system occurs in such a way that P(x,t) presents a time behavior for its width, normalization, and second moment, in full agreement with the analytic solution of the nonlinear Fokker-Planck equation. The present results provide further evidence that this system is deeply associated with nonextensive statistical mechanics.