Abstract
We consider nonequilibrium (NEQ) states such as supercooled liquids and glasses that are described with the use of internal variables. We classify the latter by the state-dependent hierarchy of relaxation times to assess their relevance for irreversible contributions. Given an observation time , we determine the window of relaxation times that divide the internal variables into active and inactive groups, the former playing a central role in the NEQ thermodynamics. Using this thermodynamics, we determine (i) a bound on the NEQ entropy and on the residual entropy and (ii) the nature of the isothermal relaxation of the entropy and the enthalpy in accordance with the second law. A theory that violates the second law such as the entropy loss view is shown to be internally inconsistent if we require it to be consistent with experiments. The inactive internal variables still play an indirect role in determining the temperature and the pressure of the system, which deviate from their external values.
Highlights
Glass, such as naturally-occurring obsidian, pumice, etc., or man-made Venetian glass, window glass, etc., is a well-known class of materials that has captured our fascination forever
We can make a defect-free glass in the laboratory for a variety of scientific and technological applications. It is an almost solid-like amorphous material that possesses no long-range atomic order and, upon heating, gradually softens as it turns into its molten state as it passes through the glass transition region normally denoted by a suitable chosen single temperature Tg in this region [1,2,3,4]
For the purpose of this article, a glass is treated merely as a nonequilibrium (NEQ) state of matter, which can be made quite homogeneous so to a good approximation, it can be treated as a thermodynamic system that is in internal equilibrium (IEQ), but not in equilibrium (EQ), as explained later (at present, it suffices to say that the entropy in an IEQ state is a state function of its state variables that include some NEQ state variables [1,2,3,4] besides those needed to specify EQ states; see [5,6,7])
Summary
Glass, such as naturally-occurring obsidian, pumice, etc., or man-made Venetian glass, window glass, etc., is a well-known class of materials that has captured our fascination forever. The relaxation time is defined as the time required for the corresponding dynamical variable to come to equilibrium with the medium; see Equation (7). Τk
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