 The instantaneous state of one system of the ensemble is specified by one point in its phase space. The state of the ensemble as a whole is therefore specified by a density function \(\varrho\) on the system’s phase space. From a technical point of view \(\varrho\) is a function just like \(f\) that we encountered in Section 1. We furthermore assume that \(\varrho\) is a probability density, reflecting the probability density of finding the state of a system chosen at random from the entire ensemble in region \(R\), so that the probability of the state being in \(R\) is \(p(R) = \int_R \varrho d\mu\). To make this more intuitive consider the following analogy. You play a special kind of darts: you fix a plank to the wall, which serves as your dart board. For some reason you know that the probability of your dart landing at a particular place on the board is given by the curve shown in Figure 7. You are then asked what the probability is that your next dart lands in the left half of the board. The answer is 1 ⁄ 2 since one half of the surface underneath the curve is on the left side. The dart board then plays the role of the system’s state space, a region of the board (here the left half) plays the role of \(R\), and throwing a dart plays the role of picking a system from the ensemble.