Statistical Mechanics in Observable System Theory: A Quasi-Axiomatic Approach
Shiro Ishikawa
I have proposed OST (Observable System Theory) as a foundational theory of system theory. Roughly speaking, OST is a theory that unifies statistics and quantum mechanics. In comparison with ordinary statistics, its main advantage is that it possesses an explicit axiomatic structure. In this sense, I have claimed the following two points:(i): OST will, in the future, become the standard understanding of statistics.(ii): OST-based quantum mechanics is the final form of von Neumann-style quantum mechanics.Statistical mechanics, however, involves microscopic states, probability distributions, Gibbs states, coarse graining, time evolution, thermodynamic limits, and so on. For this reason, a complete axiomatization of statistical mechanics is generally regarded as difficult. In the present paper, we propose a different strategy: the system-theoretical part of statistical mechanics is formulated by means of the axiomatic structure of OST, while the remaining parts are treated in the conventional way, withoutforcing them into a single axiomatic system.The aim of this paper is to understand statistical mechanics in the language of OST. In other words, the parts of statistical mechanics in which statistics has traditionally been used are here reformulated by means of OST. Thus, statistical mechanics is examined from the viewpoint of the three-term structure: state, observable, measured value. Although this is only a partial axiomatization, it nevertheless allows us to make the following claim: (iii): OST-based statistical mechanics will, in the future, become the standard understanding of statistical mechanics.This should be regarded as a corollary of (i) above. At least from the foundational viewpoint of how statistical mechanics should be read as a descriptive specification, the author believes that the OST-based understanding of statistical mechanics is more natural than the conventional one.
•May 30, 2026•0 citations