To illustrate Boltzmann’s construction of an entropy function that is defined for a microstate of a macroscopic system, we present here the simple example of the free expansion of a one dimensional gas of non-interacting point particles. The construction requires one to define macrostates, corresponding to macroscopic variables and we will discuss two specific macrostate constructions. Our results illustrate that concepts such as that of ergodicity and chaos are not as relevant as sometimes claimed, for observing macroscopic irreversibility and entropy increase. Rather, the notions of initial conditions, typicality, large numbers and coarse-graining are the important factors. We will also briefly discuss results for an interacting gas.