We will be concerned, in this chapter, with the idea of a system S that is embedded in and interacts with another system, conventionally called the environment \(E_S\) of S, which is also a system. The fact that S interacts with \(E_S\) —we will often drop the ‘S’ subscript and just call this ‘E’ when the context is clear—renders S an open system; E, by virtue of interacting with S, is also an open system. We will sometimes, beginning in Sect. 2.3 below, describe S as an “observer” of E and thus develop a generic theory of S “preparing” a state of E and then making a “measurement” of that prepared state.