A microscopic perspective on the physical foundations of continuum mechanics .1. Macroscopic states, reproducibility, and macroscopic statistics, at prescribed scales of length and time

A definition of macroscopic state for non-equilibrium situations, and at a given length scale (or pair of length-time scales) is formulated on the basis of molecular considerations. Reproducibility of experimental data is related to the length-time scales and to the intrinsic errors associated with measurement values. The choice of the microscopic phase space probability density function associated with preparation of the system is discussed in this context, and the corresponding probability density for macroscopic states is derived. Remarks are made on the concept of ''ensemble'', the apparent paradox of irreversible macroscopic behaviour in the context of time-reversal invariance of microscopic dynamics, and the notion of ''stationarity''. Published by Elsevier Science Ltd