A piece of metal remembers what you've done to it. Bend it, heat it, cool it, and it will respond differently the next time—not because of some mystical material consciousness, but because of physics that, until now, seemed to exist outside the laws of thermodynamics. This history-dependent behavior, called hysteresis, is the reason memory devices work, why certain materials can convert energy so efficiently, and why some structures remain durable under stress. Yet for centuries, scientists have struggled with a paradox: how can materials have genuine memory if thermodynamics says that a system's state is fully defined by simple variables like temperature and volume?
The puzzle matters because hysteresis appears everywhere in engineering. Yet treating it as a rogue phenomenon—outside equilibrium thermodynamics—has limited how deeply we can understand and design with it. Now Prof. Koun Shirai at the Graduate School of Engineering, The University of Osaka, has published a solution in the International Journal of Thermodynamics. His insight is deceptively simple: we've been asking the wrong question.
The standard thermodynamic view holds that if you know a solid's temperature and volume, you know everything about its state. But Shirai demonstrates that this is insufficient. Two metals at identical temperatures and volumes can behave completely differently if their atomic arrangements differ. A crystal that cooled slowly may have fewer defects than one that cooled rapidly. A metal that was previously stretched may have a different pattern of dislocations. These microscopic structures—the actual positions and configurations of atoms—matter profoundly to how the material responds.
Shirai's framework adds atomic configuration as a state variable, placing it on equal footing with temperature and volume. This single addition transforms hysteresis from a mysterious exception into a thermodynamic phenomenon that can be described and understood using the same mathematical language as reversible processes like the Carnot cycle—a cornerstone of physics since the 1820s. In both cases, a loop forms when one variable returns to its starting point while another hidden variable does not.
The key insight is that defects, dislocations, glass structures, and other microscopic arrangements are not ephemeral traces of past handling. Within their relaxation times—the timescales over which they remain stable—they function as legitimate equilibrium states that shape material behavior. This means a solid's history is not some non-physical baggage. It is encoded in its structure and can be treated thermodynamically.
The work also clarifies a fundamental difference between solids and gases. A gas's properties depend mainly on temperature and pressure; its internal structure is fluid and homogeneous. A solid is architecturally complex. Its internal energy is wired into the detailed arrangement of atoms. Therefore, any thermodynamic theory of solids must account for that architecture.
Shirai's framework does not propose a universal formula for every hysteresis loop—the landscape is too varied. Instead, it provides something more valuable: theoretical permission to treat history-dependent behavior as physics rather than as a failure of physics. This opens pathways for future research on memory materials, energy harvesting systems, and resilient structural materials. More broadly, it suggests that other complex systems exhibiting history-dependent behavior may yield to thermodynamic analysis once the right state variables are identified and named.
As Shirai puts it: "History dependence has often been taken as evidence that a solid is outside equilibrium thermodynamics. This study shows that the problem lies not in thermodynamics itself, but in how we define the state of a solid."