Glasses have long been considered nonequilibrium materials. The primary reason is their history-dependent properties: the observed properties are not uniquely determined by two state variables, temperature and volume, but are also affected by the process parameters such as the cooling rates. However, closer observations reveal that this history dependence is common in solids. The problem with the previous reasoning based on history dependence lies in the lack of effort to find a complete set of state variables that uniquely specifies the current properties, irrespective of past history. The guiding principle for identifying such variables is provided by the first law of thermodynamics, which requires that the internal energy U is a state function. The energy of a solid is determined by its detailed structure, including defect atoms. This obvious fact leads one to consider that the positions of all atoms comprising the solid are required to describe the energy. Although atom positions always fluctuate microscopically, their time averages are constant, which meets the requirement that state variables must be constant in time. Therefore, it is concluded that the complete set of equilibrium atom positions (the atom configuration), <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\bar{\textbf{R}}_{j}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mrow> <mi mathvariant="bold">R</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mi>j</mi> </msub> </math></EquationSource> </InlineEquation>, constitutes the required set of state variables for a solid. In this manner, contrary to the traditional view, hysteresis in solids can be described using standard thermodynamics methods through specifying the configuration, provided that the process is performed quasi-statically. The time constancy of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\bar{\textbf{R}}_{j}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mrow> <mi mathvariant="bold">R</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mi>j</mi> </msub> </math></EquationSource> </InlineEquation> is sustained by an energy barrier built around jth atom. The energy barrier determines the relaxation time. From this, it follows that every equilibrium state has a finite lifetime and that the notion of equilibrium of a material is always valid only within this timescale. Glasses, as well as defect states, are equilibrium states as long as their structure remains unchanged.

History Dependence in Thermodynamic Properties of Solids

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2026年5月12日

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Koun Shirai

摘要

Glasses have long been considered nonequilibrium materials. The primary reason is their history-dependent properties: the observed properties are not uniquely determined by two state variables, temperature and volume, but are also affected by the process parameters such as the cooling rates. However, closer observations reveal that this history dependence is common in solids. The problem with the previous reasoning based on history dependence lies in the lack of effort to find a complete set of state variables that uniquely specifies the current properties, irrespective of past history. The guiding principle for identifying such variables is provided by the first law of thermodynamics, which requires that the internal energy U is a state function. The energy of a solid is determined by its detailed structure, including defect atoms. This obvious fact leads one to consider that the positions of all atoms comprising the solid are required to describe the energy. Although atom positions always fluctuate microscopically, their time averages are constant, which meets the requirement that state variables must be constant in time. Therefore, it is concluded that the complete set of equilibrium atom positions (the atom configuration), $\bar{\textbf{R}}_{j}$ ${\bar{R}}_{j}$ , constitutes the required set of state variables for a solid. In this manner, contrary to the traditional view, hysteresis in solids can be described using standard thermodynamics methods through specifying the configuration, provided that the process is performed quasi-statically. The time constancy of $\bar{\textbf{R}}_{j}$ ${\bar{R}}_{j}$ is sustained by an energy barrier built around jth atom. The energy barrier determines the relaxation time. From this, it follows that every equilibrium state has a finite lifetime and that the notion of equilibrium of a material is always valid only within this timescale. Glasses, as well as defect states, are equilibrium states as long as their structure remains unchanged.