Experimental determination of Boltzmann’s constant Foreword: Progress in the experimental determination of Boltzmann’s constant

This special issue is entirely devoted to the experimental determination of Boltzmann’s constant k (also frequently noted kB to avoid the confusion with an electromagnetic wave vector modulus). Named after Ludwig Boltzmann, Austrian physicist of the XIXth century [1844–1906], this fundamental constant acts as a conversion factor from thermodynamic temperature to energy. More precisely, it has been introduced in statistical physics to link the entropy of a macroscopic system at thermodynamic equilibrium to the probability of occurrence of this state, taking into account all possible microscopic situations. The famous relation S = k log W engraved on Boltzmann’s tombstone was never expressed by Boltzmann himself with a specific constant, but this was initiated later by Planck, when he derived his black-body radiation law. This constant has therefore the same dimension as entropy and the dimensionless quantity S/k is Shannon’s information entropy [1]. Indeed, k is sometimes considered as the quantum of information [2]. Whatever the physical principles involved in the experiment, any measurement of k requires a refined control of the thermodynamic temperature and the materialisation of references of the temperature. Since metrologists are presently attempting to redefine base units of the SI (the international system of units) using fundamental physical constants [3], there is currently a great interest for new, accurate determinations of k, which could link the thermodynamic temperature unit (the kelvin) to the quantum of thermal energy and to statistical thermodynamics. The present definition of the unit “kelvin ” assigns a fixed value to the temperature of the triple point of water. It is based on a constant of nature

The Learning Curve and Annual Procedure Volume Standards for Optimum Outcomes of Transcatheter Aortic Valve Replacement: Findings From an International Registry.

The authors aimed to determine the procedural learning curve and minimum annual institutional volumes associated with optimum clinical outcomes for transcatheter aortic valve replacement (TAVR). Transcatheter aortic valve replacement (TAVR) is a complex procedure requiring significant training and experience for successful outcome. Despite increasing use of TAVR across institutions, limited information is available for its learning curve characteristics and minimum annual volumes required to optimize clinical outcomes. The study collected data for patients at 16 centers participating in the international TAVR registry since initiation of the respective TAVR program. All cases were chronologically ordered into initial (1 to 75), early (76 to 150), intermediate (151 to 225), high (226 to 300), and very high (>300) experience operators for TAVR learning curve characterization. In addition, participating institutions were stratified by annual TAVR case volume into low-volume (300) experience operators for TAVR learning curve characterization. In addition, participating institutions were stratified by annual TAVR case volume into low-volume (100) groups for comparative analysis. Procedural and 30-day clinical outcomes were collected and multivariate regression analysis performed for 30-day mortality and the early safety endpoint. A total of 3,403 patients comprised the study population. On multivariate analysis, all-cause mortality was significantly higher for initial (odds ratio [OR]: 3.83; 95% confidence interval [CI]: 1.93 to 7.60), early (OR: 2.41; 95% CI: 1.51 to 5.03), and intermediate (OR: 2.53; 95% CI: 1.19 to 5.40) experience groups compared with the very high experience operators. In addition, the early safety endpoint was significantly worse for all experience groups compared with the very high experience operators. Low annual volume ( TAVR procedures display important learning curve characteristics with both greater procedural safety and a lower mortality when performed by experienced operators. In addition, TAVR performed at low annual volume