To document the importance of open systems, let us consider some examples of active systems. Most practical engines (in the sense of machines which convert some form of energy into mechanical work) exchange matter with two or more reservoirs. To cite examples from an earlier technology (avoiding the complications of internal phase transitions or chemical reactions) we might consider the overshot water wheel (Reynolds, 1983), which operates between reservoirs of water at different gravitational potential, or the high-pressure steam engine (Dickinson, 1938), which operates between its boiler and the atmosphere, reservoirs which differ greatly in their pressure and temperature. Conspicuously absent from a list of economically significant engines are systems which operate upon the Carnot model of a closed system in purely thermal contact with its reservoirs.
A technology of more current interest is electronics, whose systems are usually arranged such that a ``power supply'' maintains constant voltages ( i.e., chemical potentials for electrons) on two or more ``buses'' (see, for example, Horowitz and Hill, 1980). The ``circuits'' (such as logical gates or analog amplifiers) which perform the intended functions of the system are connected to, and conduct current between, the buses. Each bus is an electron reservoir, and the performance of the system's power supply is judged by how nearly these reservoirs approach the ideal behavior of no change in chemical potential (voltage) as particles are exchanged (current is drawn).
The example of electronics points out that the distinction between a closed and an open system depends upon how one chooses to partition the universe into the system of interest and ``everything else.'' (Such a partitioning is implicit in the analysis of every physical problem.) To demonstrate this point, let us examine the etymology of the term circuit. As used in the preceding paragraph, circuit means ``an assemblage of electronic elements'' (Woolf, 1981), which is most often open with respect to electron flow. This usage of the term is now much more common among electrical engineers than the original meaning, ``the complete path of an electric current including usually the source of electric energy,'' (Woolf, 1981) which implies a closed system with respect to electron flow. It is no accident that the usage of the word circuit has evolved in this manner. Early in the development of electrical technology, a useful system [such as the electromagnetic telegraph (Marland, 1964)] was composed of at most a few topologically closed ``circuits,'' and the closure of the current path was a central concern. As the complexity of electrical systems increased, the convention of organizing a system in terms of a power supply and its buses was developed. This provided a common segment for all the current paths, and the attention of the engineer focused on the remaining, ``interesting,'' segment, that which contained the active devices (and the term circuit came to be applied to such a segment). However, by focusing on only a segment of the current path, one had to deal with an open system, rather than a closed one.
The physics of closed systems is certainly simpler than that of open systems, because closed systems obey global conservation laws, while open systems, in general, do not. In the well-established techniques of physical theory one often encounters artifices, usually in the form of periodic boundary conditions, which assure the closure of the theoretical model, if not of the system itself. The point of the present discussion is that it is frequently necessary to partition a complex system (which might reasonably be regarded as closed) into smaller components which, viewed individually, must be regarded as open. Thus, the more applied disciplines of the physical sciences must often deal at some level with the concept of an open system.
There are many established techniques for dealing with open systems in fields such as fluid dynamics, neutron transport, and electronics. All these fields are concerned with the transport of (usually) conserved particles. The transport phenomena are described by transport equations at a kinetic or hydrodynamic level which are either differential or integro-differential equations. Such equations require boundary conditions, and it is in these boundary conditions that the openness of a system is described. In the computation of the flow around an airfoil, one must supply ``upstream'' and ``downstream'' boundary conditions (Roache, 1976, ch. III, sec. C). In electronics the connection to the external circuit is accomplished by some sort of contact. In solid-state electronics the most frequently used type of contact is the ohmic contact, an interface between a metallic conductor and (usually) a semiconductor which permits electrons to pass freely. Because the ohmic contact is a critical component of solid-state technology, most work on such interfaces has been directed toward their fabrication and characterization (Milnes and Feucht, 1972). The theoretical representation of such contacts by boundary conditions has been a part of the analysis of semiconductor device problems since the beginning of semiconductor technology (Bardeen, 1949; Shockley, 1949). The current practice of using boundary conditions to model contacts is discussed in detail by Selberherr (1984, sec. 5.1).