1. Numerical statistical physics of sets of atoms

1.1 Statistical sets. Taking averages

Statistical mechanics provides the link between a microscopic world described as a collection of interacting particles, or ensemble, and our macroscopic world, or more precisely the measurable properties at our scale of a homogeneous volume element of a given substance modeled by this ensemble.

The essential operation here is to take the average, extended to the whole, of an elementary physical scalar or vector quantity that can be associated with each particle: total energy, potential energy, kinetic energy, position, momentum.

An assembly is defined by a set of imposed macroscopic state variables, such as energy E, temperature T, number of particles N, volume V, pressure P, chemical potential µ....