A rigourous demonstration of the validity of Boltzmann's scenario for the spatial homogenization of a freely expanding gas and the equilibration of the Kac ring

Boltzmann provided a scenario to explain why individual macroscopic systems composed of a large number $N$ of microscopic constituents are inevitably (i.e., with overwhelming probability) observed to approach a unique macroscopic state of thermodynamic equilibrium, and why after having done so, they are then observed to remain in that state, apparently forever. We provide here rigourous new results that mathematically prove the basic features of Boltzmann's scenario for two classical models: a simple boundary-free model for the spatial homogenization of a non-interacting gas of point particles, and the well-known Kac ring model. Our results, based on concentration inequalities that go back to Hoeffding, and which focus on the typical behavior of individual macroscopic systems, improve upon previous results by providing estimates, exponential in $N$, of probabilities and time scales involved

Dynamical Mechanisms Leading to Equilibration in Two-component Gases

Demonstrating how microscopic dynamics cause large systems to approach thermal equilibrium remains an elusive, longstanding, and actively pursued goal of statistical mechanics. We identify here a dynamical mechanism for thermalization in a general class of two-component dynamical Lorentz gases and prove that each component, even when maintained in a nonequilibrium state itself, can drive the other to a thermal state with a well-defined effective temperature

The Nature and Role of Primary Certified Isotopic Reference Materials - A Tool to Underpin Isotopic Measurements on a Global Scale

A Chapter that focuses on isotopic reference materials with certified values that are traceable to SI, and explains how they can be produced. An overview is given of cases where such materials have already been realised.JRC.D.4-Isotope measurement

A New Measurement of the 241-Pu Half-Life Using Isotope Mass Spectrometry.

The half-life of 241-Pu for beta decay has been determined on an iniyially 93% isotopically enriched material by measuring the decreasing amount ratio n(241Pu)/n (240Pu) as a function of time over more then twenty years. Over the same period the decrease of this ratio was measured relative to the amount ratio n(240Pu)/n (239 Pu) in a ratio-of-ratio measurement which allowed for correction of isotopic effects in the ion source whilst decay of 240-Pu (half-life=6553 a) and 239-Pu (half-life=24 110 a) were taken into account. The resulting value for the 241-Pu half-life is 14.290+- 0.006 a (expanded uncertainty with coverage factor k=2). The slight difference found with the half life value as measured by us on the same material in the period 1976- 1981 is discussed.JRC.D-Institute for Reference Materials and Measurements (Geel

Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir

Rigorous derivations of the approach of individual elements of large isolated systems to a state of thermal equilibrium, starting from arbitrary initial states, are exceedingly rare. This is particularly true for quantum mechanical systems. We demonstrate here how, through a mechanism of repeated scattering, an approach to equilibrium of this type actually occurs in a specific quantum system, one that can be viewed as a natural quantum analog of several previously studied classical models. In particular, we consider an optical mode passing through a reservoir composed of a large number of sequentially-encountered modes of the same frequency, each of which it interacts with through a beam splitter. We then analyze the dependence of the asymptotic state of this mode on the assumed stationary common initial state $\sigma$ of the reservoir modes and on the transmittance $\tau=\cos\lambda$ of the beam splitters. These results allow us to establish that at small $\lambda$ such a mode will, starting from an arbitrary initial system state $\rho$, approach a state of thermal equilibrium even when the reservoir modes are not themselves initially thermalized. We show in addition that, when the initial states are pure, the asymptotic state of the optical mode is maximally entangled with the reservoir and exhibits less nonclassicality than the state of the reservoir modes

Absolute Measurements of Isotope Amount Ratios on Gases Part II: Application of the Measurement Models Developed on Real Gases

The power of the theoretical formalisms based on concepts from kinetic gas theory described in Part I of this series, is demonstrated in isotope measurement results obtained for three different gases: CO2, SiF4 gas highly enriched in the 28Si isotope and a high purity neon gas of natural isotopic composition. The measurement procedure as described in this paper enables to detect various (small) anomalies in the gas mass spectrometer during the ion current measurements thus creating the opportunity to correct for them. Using these concepts which govern the isotope fractionation of the gas in the mass spectrometer and performing a calibration by means of synthesized values for isotope amount ratios, SI traceable values in terms of the derived measurement unit mol/mol can be obtained.JRC.D.4-Isotope measurement

Absolute Isotope Amount Ratio Measurements on Gases Part I: Measurements of Isotope Amount Ratios - Basic Theory

A basic measurement model and corresponding measurement function for measuring isotope amount ratios on various gases is described and discussed. The approach is different from the one used in delta measurements not only by the method but also by the nature of the results. Performed on similar types of 'hardware' (a gas isotope ratio mass spectrometer) Isotope Amount Ratio Measurements ('IARM') are not intended to replace the traditional (delta) isotope measurements but to complement them: providing 'absolute' isotope amount ratio values when there is a need for them. The basic theory is discussed while in a subsequent paper, illustrations by experimental values will be described. The measurement functions used in performing 'IARM' describe a transparent and metrologically traceable relationship between an isotope amount ratio of an element (the quantity intended to be measured i.e. the 'measurand') to its measured ion current ratio (the quantity subject to measurement), based on the gas flow dynamics in the gas inlet system of the mass spectrometer and due consideration of isotope fractionation effects.JRC.D.4-Isotope measurement

Metrology in Chemistry: Status Report of Lithuania.

Abstract not availableJRC.D-Institute for Reference Materials and Measurements (Geel