Phase space is a good model of what we are interested in when we talk about a certain range of possibilities. Not all possibilities can be captured in phase space, but, for certain purposes, many of the interesting ones can be. In this chapter, I will introduce the idea that we have not yet seen the most powerful and useful application of phase space: to model certain types of probabilities or chances.

The leaking tyre

You wake up to find yourself in a closed room, isolated from outside causal influence. In the middle of the room is a bicycle tyre. Because all else is quiet, you can hear that the tyre is hissing very gently, and as you go over to it, you are able to locate the small stream of air that is leaking out of a tiny hole, producing the noise. You judge, by a squeeze of the tyre, that it will take some time before the air will stop hissing out of the tyre.

What is the macro-condition of the room right now? It is one in which there is a large volume of gas at relatively low pressure, and a small volume of gas in the tyre, at relatively high pressure. Moreover, there is a small aperture between these two volumes of gas.