TITLE:
Ergodic Hypothesis and Equilibrium Statistical Mechanics in the Quantum Mechanical World View
AUTHORS:
Shiro Ishikawa
KEYWORDS:
The Copenhagen Interpretation; Probability; Operator Algebra; Ergodic Theorem; Quantum and Classical Measurement Theory; Liouville’s Theorem; The Law of Increasing Entropy
JOURNAL NAME:
World Journal of Mechanics,
Vol.2 No.2,
April
26,
2012
ABSTRACT: 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”.