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.