A Pedagogical Intrinsic Approach to Relative Entropies as Potential Functions of Quantum Metrics: the qq-zz Family

The so-called $q$-z-\textit{R\'enyi Relative Entropies} provide a huge two-parameter family of relative entropies which includes almost all well-known examples of quantum relative entropies for suitable values of the parameters. In this paper we consider a log-regularized version of this family and use it as a family of potential functions to generate covariant $(0,2)$ symmetric tensors on the space of invertible quantum states in finite dimensions. The geometric formalism developed here allows us to obtain the explicit expressions of such tensor fields in terms of a basis of globally defined differential forms on a suitable unfolding space without the need to introduce a specific set of coordinates. To make the reader acquainted with the intrinsic formalism introduced, we first perform the computation for the qubit case, and then, we extend the computation of the metric-like tensors to a generic $n$-level system. By suitably varying the parameters $q$ and $z$, we are able to recover well-known examples of quantum metric tensors that, in our treatment, appear written in terms of globally defined geometrical objects that do not depend on the coordinates system used. In particular, we obtain a coordinate-free expression for the von Neumann-Umegaki metric, for the Bures metric and for the Wigner-Yanase metric in the arbitrary $n$-level case.Comment: 50 pages, 1 figur

Bipolar switching in chalcogenide phase change memory

Phase change materials based on chalcogenides are key enabling technologies for optical storage, such as rewritable CD and DVD, and recently also electrical nonvolatile memory, named phase change memory (PCM). In a PCM, the amorphous or crystalline phase affects the material band structure, hence the device resistance. Although phase transformation is extremely fast and repeatable, the amorphous phase suffers structural relaxation and crystallization at relatively low temperatures, which may affect the temperature stability of PCM state. To improve the time/temperature stability of the PCM, novel operation modes of the device should be identified. Here, we present bipolar switching operation of PCM, which is interpreted by ion migration in the solid state induced by elevated temperature and electric field similar to the bipolar switching in metal oxides. The temperature stability of the high resistance state is demonstrated and explained based on the local depletion of chemical species from the electrode region

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

International audienceWe formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model

Association of kidney disease measures with risk of renal function worsening in patients with type 1 diabetes

Background: Albuminuria has been classically considered a marker of kidney damage progression in diabetic patients and it is routinely assessed to monitor kidney function. However, the role of a mild GFR reduction on the development of stage 653 CKD has been less explored in type 1 diabetes mellitus (T1DM) patients. Aim of the present study was to evaluate the prognostic role of kidney disease measures, namely albuminuria and reduced GFR, on the development of stage 653 CKD in a large cohort of patients affected by T1DM. Methods: A total of 4284 patients affected by T1DM followed-up at 76 diabetes centers participating to the Italian Association of Clinical Diabetologists (Associazione Medici Diabetologi, AMD) initiative constitutes the study population. Urinary albumin excretion (ACR) and estimated GFR (eGFR) were retrieved and analyzed. The incidence of stage 653 CKD (eGFR < 60 mL/min/1.73 m2) or eGFR reduction > 30% from baseline was evaluated. Results: The mean estimated GFR was 98 \ub1 17 mL/min/1.73m2 and the proportion of patients with albuminuria was 15.3% (n = 654) at baseline. About 8% (n = 337) of patients developed one of the two renal endpoints during the 4-year follow-up period. Age, albuminuria (micro or macro) and baseline eGFR < 90 ml/min/m2 were independent risk factors for stage 653 CKD and renal function worsening. When compared to patients with eGFR > 90 ml/min/1.73m2 and normoalbuminuria, those with albuminuria at baseline had a 1.69 greater risk of reaching stage 3 CKD, while patients with mild eGFR reduction (i.e. eGFR between 90 and 60 mL/min/1.73 m2) show a 3.81 greater risk that rose to 8.24 for those patients with albuminuria and mild eGFR reduction at baseline. Conclusions: Albuminuria and eGFR reduction represent independent risk factors for incident stage 653 CKD in T1DM patients. The simultaneous occurrence of reduced eGFR and albuminuria have a synergistic effect on renal function worsening

Associations between depressive symptoms and disease progression in older patients with chronic kidney disease: results of the EQUAL study

Background Depressive symptoms are associated with adverse clinical outcomes in patients with end-stage kidney disease; however, few small studies have examined this association in patients with earlier phases of chronic kidney disease (CKD). We studied associations between baseline depressive symptoms and clinical outcomes in older patients with advanced CKD and examined whether these associations differed depending on sex. Methods CKD patients (>= 65 years; estimated glomerular filtration rate <= 20 mL/min/1.73 m(2)) were included from a European multicentre prospective cohort between 2012 and 2019. Depressive symptoms were measured by the five-item Mental Health Inventory (cut-off <= 70; 0-100 scale). Cox proportional hazard analysis was used to study associations between depressive symptoms and time to dialysis initiation, all-cause mortality and these outcomes combined. A joint model was used to study the association between depressive symptoms and kidney function over time. Analyses were adjusted for potential baseline confounders. Results Overall kidney function decline in 1326 patients was -0.12 mL/min/1.73 m(2)/month. A total of 515 patients showed depressive symptoms. No significant association was found between depressive symptoms and kidney function over time (P = 0.08). Unlike women, men with depressive symptoms had an increased mortality rate compared with those without symptoms [adjusted hazard ratio 1.41 (95% confidence interval 1.03-1.93)]. Depressive symptoms were not significantly associated with a higher hazard of dialysis initiation, or with the combined outcome (i.e. dialysis initiation and all-cause mortality). Conclusions There was no significant association between depressive symptoms at baseline and decline in kidney function over time in older patients with advanced CKD. Depressive symptoms at baseline were associated with a higher mortality rate in men

Covariant momentum map thermodynamics for parametrized field theories

A general-covariant statistical framework capable of describing classical fluctuations of the gravitational field is a thorny open problem in theoretical physics, yet ultimately necessary to understand the nature of the gravitational interaction, and a key to quantum gravity. Inspired by Souriau's symplectic generalization of the Maxwell-Boltzmann-Gibbs equilibrium in Lie group thermodynamics, we investigate a space-time-covariant formulation of statistical mechanics for parametrized first-order field theories, as a simplified model sharing essential general covariant features with canonical general relativity. Starting from a covariant multi-symplectic phase space formulation, we define a general-covariant notion of Gibbs state in terms of the covariant momentum map associated with the lifted action of the diffeomorphisms group on the extended phase space. We show how such a covariant notion of equilibrium encodes the whole information about symmetry, gauge and dynamics carried by the theory, associated with a canonical spacetime foliation, where the covariant choice of a reference frame reflects in a Lie algebra-valued notion of local temperature. We investigate how physical equilibrium, hence time evolution, emerges from such a state and the role of the gauge symmetry in the thermodynamic description