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 experimen tal data is related to the length-time scales and to the intrinsic err ors associated with measurement values. The choice of the microscopic phase space probability density function associated with preparation o f the system is discussed in this context, and the corresponding proba bility density for macroscopic states is derived. Remarks are made on the concept of ''ensemble'', the apparent paradox of irreversible macr oscopic behaviour in the context of time-reversal invariance of micros copic dynamics, and the notion of ''stationarity''. Published by Elsev ier Science Ltd