Archive of historical materials
Irreversible Property of Quantum Mechanical Ensemble
OU1935-A3 (9 pages) Date: June 13, 1935
Based on the quantum mechanical principles, Yukawa tried to understand the temporal irreversibility of a macroscopic system (with enormous degrees of physical freedom), which is known as “the law of entropy increase.” Quantum mechanics was born and developed in 1925 to 1926, and immediately after that, John von Neumann attempted to refine the mathematical foundations of quantum mechanics. In 1932, von Neumann wrote a book titled “Die Mathematische Grundlagen der Quantenmechanik” (English translation: Mathematical Foundations of Quantum Mechanics). In this book, he introduced the entropy equation that used a density matrix, which formed the basis for modern quantum statistical mechanics. Yukawa used von Neumann’s entropy equation for understanding how irreversibility emerges. That was a pioneering idea in Japan at that time, when there was hardly anyone in Japan who were able to understand the relationship between quantum mechanics and statistical mechanics.
When von Neumann’s book was translated in Japanese and published in a later year (1957), Yukawa wrote the preface of the book. In the preface, he wrote: “In this book, von Neumann not only clarifies the mathematical foundations of quantum mechanics, but also describes his detailed analysis of the observation problem and takes a further step by attempting to reconstruct the quantum statistical mechanics” and “Why the Japanese translation of this book was not published until now is a mystery to me.” (Written by Yutaka Hosotani)
