The University of Osaka researcher shows that solid-state hysteresis can be described using thermodynamic state variables

Osaka, Japan - Many solid materials “remember” their past. A piece of metal may respond differently after being stretched, heated, or cooled, and memory materials rely precisely on this kind of history-dependent behavior. This phenomenon, known as hysteresis, is central to technologies such as memory devices, energy conversion materials, and durable structural materials.

However, hysteresis has long posed a problem for thermodynamics. In conventional thinking, the state of a material should be described by state variables, such as temperature and volume. But in solids, the same temperature and volume can correspond to different material properties depending on the material’s past treatment. For this reason, hysteresis has traditionally been treated as a nonequilibrium phenomenon, outside the standard framework of thermodynamics.

Prof. Koun Shirai, at the Graduate School of Engineering, The University of Osaka, has now shown that hysteresis in solids can be described thermodynamically by reconsidering what counts as an equilibrium state and what variables are needed to define the state of a solid.

The study, published in International Journal of Thermophysics, argues that the difficulty arises because temperature and volume alone are not enough to specify the state of a solid. Instead, the complete state of a solid must include its atomic configuration - the time-averaged equilibrium positions of all atoms making up the material. In other words, history dependence does not mean that thermodynamics fails. It means that some necessary state variables have been overlooked.

A common way to describe hysteresis is to say that a material’s response, Y, depends on an input, X, in a way that forms a loop. But Shirai points out that this description is incomplete. A loop can also appear in reversible thermodynamic processes, such as the Carnot cycle. The essential issue is that another hidden variable, Z, changes during the cycle. Even if X and Y return to their original values, Z may not.

The study identifies this hidden variable as the atomic configuration of the solid. Defects, dislocations, glass structures, and other microscopic arrangements can remain stable over finite timescales and influence material properties. These configurations are not merely traces of past processes; within their relaxation times, they can be treated as equilibrium states.

This approach also clarifies why solids differ from gases. For gases, a small number of macroscopic state variables is often sufficient. For solids, however, the internal energy depends on detailed structure. Therefore, a thermodynamic description of solids must include atomic positions as state variables.

The work does not provide a simple formula for every hysteresis loop. Instead, it establishes a more fundamental point - hysteresis can, in principle, be described using thermodynamic variables, provided that the relevant atomic configuration is included and the process is considered quasi-statically.

Because hysteresis is widely used in engineering, this theoretical foundation could support future research on memory materials, energy conversion systems, and other solid-state technologies. More broadly, the study suggests that history-dependent behavior in complex systems may be approached within thermodynamics when the correct state variables are identified.

“History dependence has often been taken as evidence that a solid is outside equilibrium thermodynamics,” says Prof. Shirai. “This study shows that the problem lies not in thermodynamics itself, but in how we define the state of a solid.”

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The article, “History dependence in thermodynamic properties of solids,” was published in International Journal Thermophysics at DOI: https://doi.org/10.1007/s10765-026-03763-1

About The University of Osaka
The University of Osaka was founded in 1931 as one of the seven imperial universities of Japan and is now one of Japan's leading comprehensive universities with a broad disciplinary spectrum. This strength is coupled with a singular drive for innovation that extends throughout the scientific process, from fundamental research to the creation of applied technology with positive economic impacts. Its commitment to innovation has been recognized in Japan and around the world. Now, The University of Osaka is leveraging its role as a Designated National University Corporation selected by the Ministry of Education, Culture, Sports, Science and Technology to contribute to innovation for human welfare, sustainable development of society, and social transformation.
Website: https://resou.osaka-u.ac.jp/en