Researchers have developed a quantum-mechanical framework that establishes the law of increasing entropy, a central expression of the second law of thermodynamics. The result, announced by the University of Tokyo on November 4, addresses a long-standing question about how the rules governing microscopic quantum systems connect with the behaviour of large-scale physical systems.
The collaborative research involved scientists associated with RIKEN, the University of Tokyo and the University of Osaka. The team developed a way to define thermal equilibrium, thermodynamic operations and entropy using macroscopic physical quantities within quantum mechanics.
According to the University of Tokyo’s announcement, the researchers proved that the law of increasing entropy holds for quantum states representing thermal equilibrium under the framework they established.
The work was published in the journal PRX Quantum on November 3, corresponding to November 4 in Japan Standard Time.
Why the second law matters
The second law of thermodynamics is one of the foundational principles of physics. In a common formulation, it states that the total entropy of an isolated system does not decrease over time.
Entropy is often described as a measure of disorder, although that description is incomplete. In physics, entropy is a quantity used to characterise the number of microscopic arrangements compatible with a system’s macroscopic state and the direction of thermodynamic processes.
The second law helps explain why many everyday processes have a preferred direction. Heat naturally flows from a warmer object to a cooler one under ordinary conditions. A gas spreads through an available space rather than spontaneously gathering into one small region. These processes are associated with an increase in entropy.
The law is central to understanding heat engines, refrigerators, energy conversion and the limits of how efficiently energy can be used.
Quantum mechanics, meanwhile, describes the behaviour of matter and energy at microscopic scales. It governs particles, atoms and other systems whose properties cannot always be explained using classical physics.
Connecting these two descriptions has been an important theoretical challenge.
The difficulty of connecting quantum mechanics and thermodynamics
Quantum mechanics allows a wide range of mathematical operations on quantum states. But when quantum states are interpreted as thermal equilibrium states, not every mathematically allowed operation corresponds to a physically meaningful thermodynamic process.
This creates a potential problem. If the framework used to describe quantum operations is too broad, it can appear to permit changes that conflict with the second law.
The research team sought to address this issue by establishing a more physically meaningful way to describe equilibrium states and operations.
Rather than treating every abstract quantum operation as a thermodynamic process, the researchers used macroscopic physical quantities to formulate the relevant concepts.
The University of Tokyo’s summary says the framework was used to define thermal equilibrium states, thermodynamic operations and entropy in quantum-mechanical terms. The researchers then proved that the law of increasing entropy follows for any quantum states representing thermal equilibrium within the framework.
The result provides a more rigorous connection between microscopic quantum descriptions and macroscopic thermodynamic behaviour.
What the researchers established
The central result is a mathematical proof that the law of increasing entropy can be derived from quantum mechanics under the conditions and definitions used in the study.
This is important because thermodynamics is often introduced as a theory of large systems, while quantum mechanics describes the microscopic components from which those systems are made.
The research addresses how a principle observed at the macroscopic level can be consistently represented within a quantum framework.
The finding should not be interpreted as a claim that every aspect of thermodynamics has now been solved or that the second law has been experimentally overturned. The researchers report a theoretical result: a proof within a defined framework for quantum states representing thermal equilibrium.
The distinction matters. A mathematical derivation can strengthen the foundations of a theory, but it does not automatically create a new practical device or demonstrate an immediate technological application.
Potential relevance to quantum technologies
The researchers say the framework may contribute to a better understanding of how thermodynamics emerges from quantum mechanics. They also suggest it could provide guidelines for controlling quantum systems.
This is relevant to the development of quantum technologies, where researchers need to understand how quantum states behave under operations and how energy and information move through a system.
Quantum computers, for example, rely on controlling delicate quantum states. Their operation is affected by interactions with the environment, unwanted disturbances and energy exchange. Understanding the thermodynamic constraints on quantum systems is part of the wider effort to improve their design and operation.
The new framework may help researchers reason more precisely about which operations are physically meaningful and how equilibrium concepts should be represented.
However, the announcement does not claim that the work directly improves the performance of existing quantum computers. Its immediate contribution is theoretical, providing a foundation that other researchers may build upon.
A collaboration across research institutions
The research involved Yuya Chiba, Tatsushi Hamazaki, Yasushi Yoneda and Akira Shimizu, with institutional links to RIKEN and universities in Japan.
The University of Tokyo’s announcement notes that the findings were selected by the American Physical Society as a paper for press release. The study appeared in PRX Quantum under the title “Second Law of Thermodynamics in Closed Quantum Many-Body Systems.”
The involvement of researchers from multiple institutions reflects the interdisciplinary nature of the problem. The work sits at the intersection of quantum statistical mechanics, mathematical physics and thermodynamics.
Why the result is worth watching
The second law is often presented as a settled principle of physics. The new research does not replace that principle; instead, it addresses how it can be derived from a more fundamental quantum description.
That distinction makes the result significant for theoretical physics. It helps clarify the relationship between the microscopic laws governing quantum systems and the macroscopic rules that describe heat, energy and equilibrium.
The next step will be for other researchers to examine the framework, explore its implications and determine how it can be applied to different quantum systems.
For now, the study offers a rigorous theoretical bridge between two major areas of physics. It is a contribution to the foundations of quantum thermodynamics rather than an immediate consumer technology breakthrough.