DATE2026.11.04 #Press Releases

The Second Law of Thermodynamics is proven from Quantum Mechanics

Disclaimer: machine translated by DeepL which may contain errors.

— Established a Quantum Mechanical Framework for Thermal Equilibrium and Operations Based on Macroscopic Physical Quantities —

Summary

Yuya Chiba, Special Researcher in Basic Science (at the time of the research; currently a Visiting Researcher) at the Hamazaki Non-equilibrium Quantum Statistical Mechanics Institute for Frontier Research, RIKEN White-Eyebrow Research Team, RIKEN (RIKEN), andTatsushi Hamazaki, Team Leader of the RIKEN Hakubi Research Team (Senior Researcher, Division of Mathematical Foundations, Center for Mathematical Creativity), Yasushi Yoneda, Special Researcher in Basic Science (at the time of the research; currently a Visiting Researcher) of the Quantum Computing Theory Research Team at the Quantum Computer Research Center, Akira Shimizu, Project Researcher and Emeritus Professor at the Institute for Photon Science and Technology, Graduate School of Science, The University of Tokyo (Project Professor at the Center for Quantum Information and Quantum Biology (QIQB), The University of Osaka), have constructed a rigorous quantum-mechanical framework that represents  “thermal equilibrium” and “ operations” in thermodynamics. Using this framework, the group proved that the “law of increasing entropy” — the most significant expression of the second law of thermodynamics— holds true.

These research findings are expected to lead to a better understanding of how thermodynamics— a law of the macroscopic world— emerges from quantum mechanics— a law of the microscopic world—and, furthermore, to provide guidelines for controlling quantum systems.

In recent years, it has been revealed that many states in quantum mechanics correspond to thermal equilibrium states in thermodynamics. However, when various operations—as traditionally conceived in quantum mechanics— are applied to these states, there are cases that contradict the second law of thermodynamics; consequently, the consistency between quantum mechanics and thermodynamics has been a fundamental issue.

In this study, the collaborative research group proposed macroscopically-meaningful physical quantities and used them to formulate thermal equilibrium states, thermodynamic operations, and entropy in terms of quantum mechanics. As a result, they have succeeded for the first time in proving that the law of increasing entropy— a fundamental expression of the second law of thermodynamics— can be derived from quantum mechanics for any quantum states that represent thermal equilibrium.

This research was published in the online edition of the scientific journal *PRX Quantum* (November 3: November 4, Japan Standard Time). The findings of this study were selected by the American Physical Society as a paper for press release.

Possible transitions for macro- and micro-operations, and transitions whose impossibility was proven in this study
(Image: Issey Takahashi)

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