11.3.2: Interaction Model

The reason for our partition model is that we want to control interaction between the system and its environment. Different physical systems would have different modes of interaction, and different mechanisms for isolating different parts. Here is described a simple model for interaction of magnetic dipoles that are aligned in a row. It is offered as an example.

Suppose that the apparatus that holds the magnetic dipoles allows adjacent dipoles to influence each other. This influence might be to cause one dipole to change from up to down or vice versa. Naturally, if one dipole influences its neighbor, then its neighbor at the same time influences it. It is reasonable to suppose that if one dipole changes its status from, say, up to down, then the neighbor that is interacting with it should change its status in the opposite direction. The effect is that the two dipoles exchange their orientations. The total number of dipoles oriented in each direction stays fixed.

Consider two adjacent dipoles that exchange their orientations—the one on the left ends up with the orientation that the one on the right started with, and vice versa. There are only a few different cases.

First, if the two dipoles started with the same orientation, nothing would change. On the other hand, if the two dipoles started with different orientations, the effect would be that the pattern of orientations has changed–the upward orientation has moved to the left or the right. This has happened even though the dipoles themselves have not moved. Since the energy associated with the two possible alignments is different, there has been a small change in the location of the energy, even though the total energy is unchanged.

Second, if both dipoles are in the system, or both are in the environment, then energy may have shifted position within the system or the environment, but has not moved between them.

Third, if the two dipoles started with different alignment, and they are located one on each side of the boundary between the system and the environment, then energy has flowed from the system to the environment or vice versa. This has happened not because the dipoles have moved, but because the orientations have moved.

Energy that is transferred to or from the system as a result of interactions of this sort is referred to as heat. A formula for heat in terms of changes of probability distribution is given below.

Sometimes this kind of a process is referred to as “mixing” because the effect is similar to that of different kinds of particles being mixed together. However, in this analogy the dipoles do not move; it is their pattern of orientations or their microscopic energies that have moved and mixed.

Let us assume that we can, by placing or removing appropriate barriers, either inhibit or permit this process. For example, the process might be inhibited by simply moving the system away from its environment physically. Energy conversion devices generally use sequences where mixing is encouraged or discouraged at different times.