Macroscopic Prediction

Our topic is the principles for prediction of macroscopic phenomena in general, and the relation to microphenomena. Although physicists believe that we have understood the laws of microphysics quite well for fty years, macrophenomena are observed to have a rich variety that is very hard to understand. We see not only lifeless thermal equilibrium and irreversible approaches to it, but lively behavior such as that of cyclic chemical reactions, lasers, self{organizing systems, biological systems. On a di erent plane, we feel that we understand the general thinking and economic motivations of the individual people who are the micro{elements of a society; yet millions of those people combine to make a macroeconomic system whose oscillations and unstable behavior, in de ance of equilibrium theory, leave us bewildered. Governments seem helpless to understand what is happening well enough to predict it, much less control it. Why is it that knowledge of microphenomena does not seem su cient to understand macrophenomena? Is there an extra general principle needed for this? Our message is that such a general principle is indeed needed and already exists, having been given by J. Willard Gibbs over 100 years ago; but it is not fully recognized in the current thinking of either statistical mechanics or economics. A macrostate has a crucially important further property (entropy) that is not determined by the microstate. We hope to discuss the problem in some generality, give a mathematical scheme embodying that principle, and show a few of its consequences. Of course, any particular mathematical scheme will apply only in a particular area, so we do not want to take a provincial viewpoint tied too strongly to the mathematics. Fortunately, understanding of the problem has advanced to the point where it is possible to explain the principles in a very simple way with almost no mathematics. Only from the simplest viewpoint can one see the full range of application of a principle.