"Physics is the prime example of the exact sciences, and statistical mechanics constitute one of the important bases of physics. Now, if one is told that the foundation of statistical mechanics is not entirely clear, he/she would feel rather astounded and puzzled. Being one of those engaged in this discipline, the writer feels a little embarrassed to admit this, but it is indeed a fact. There is, nevertheless, no doubt about the validity of statistical mechanics. When one is concerned with its application, it would be better if one uses it as much as possible without being too disturbed. The problem here is how to justify the principle of equal weight. There are rather many physicists who are not satisfied with the ergodic theorem. The mathematical proof of this theorem is too general. It does not make use of the characteristic property of dynamical systems in physics, such as we deal with in statistical mechanics. We tend to think, therefore, that in this theory, we are not really grasping the physical circumstances which make statistical mechanics successful. One would feel that the basis for relating the value of actual observation to that which has to do with probability lies in the fact that an actual system consists of a large number of particles. Although this intuition is probably true, it has not been fully clarified. Basic problems such as this are not raised just from philosophical interest alone. Indeed, we cannot avoid these problems when we want to advance the study of statistical mechanics to fields thus far unexplored, such as the problem of irreversible processes."

Fragmento extraído del libro de Ryogo Kubo, "Statistical Mechanics", Wiley, Nueva York (1965).