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 logW 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, assumed to be uniform and sustainable, as it is the case for the definition of the second based on the period of a transition in atomic caesium. However, the practical realization of the unit still requires a kind of artifact. One has to build cells where the triple point of water can be obtained and, indeed, the precise international recommendations for doing this have evolved over time. A new definition involving a fixed numerical value of k would also have the advantage of being directly applicable to any primary measurement method of the thermodynamic temperature, such as pyrometry. However, to obtain the full benefit from such a new definition, it is first necessary to obtain a sufficiently low relative uncertainty on the value of the Boltzmann constant, typically of the order of 10−6 and, of course, an international consensus on the numerical value. In practice, only a few physical principles can be applied to set up an experiment aiming at the determination of k. In most cases, one has to link a macroscopic observable to the microscopic thermal motion of particles at the thermodynamic equilibrium. The equation of state of an ideal gas gives directly access to the gas constant R, and thus to k. The velocity of sound in gases relies on how mechanical waves can propagate in the medium, thanks