Quantum statistical mechanics

Qian Shang-Wu, Xu Lai-Zi

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.

Carl S. Helrich

Kenneth S. Schmitz

Shiro Ishikawa

In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statistical mechanics? 2): Is the ergodic hypothesis related to equilibrium statistical mechanics? Note that these problems are not yet answered, since there are several opinions for the formulation of equilibrium statistical mechanics. In order to answer the above questions, we first introduce measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. And we propose the measurement theoretical foundation of equili-brium statistical mechanics, and further, answer the above 1) and 2), that is, 1) is “No”, but, 2) is “Yes”.

Francesco R. Ruggeri

In physics, there are deterministic theories such as classical mechanics and statistical theories such as classical statistical mechanics and quantum mechanics. Many interpretations are applied to statistical theories and there is sometimes debate as to the application of such theories in various physical scenarios. In a previous note, we considered cycling due to exp(iEt) in quantum mechanics and tried to argue that such cycling may also appear in statistical mechanics. We made use of the example of the ground state of the quantum oscillator which has a quantum mechanical density of the same form as the classical statistical mechanical result. In this note, we wish to consider the idea of cycling in statistical mechanics using some simple examples. In addition, we wish to also examine the notion of losing information to pass from a deterministic theory to a statistical one. Finally, we wish to consider some possible aspects of the classical statistical density in a potential. It seems that even in classical statistical mechanics, the picture presented by the ‘averaging’ may actually be quite different from the physical scenario which may contain deterministic behavior which is lost in the calculation of statistical results.

T. Banks