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- Title
Glass thermodynamics: Clausius theorem and a new tensorial definition of temperature.
- Authors
Akira Takada; Conradt, Reinhard; Richet, Pascal
- Abstract
This paper aims at unifying the statistical mechanics and thermodynamics of glass through a new extended definition of temperature. Along with new insights into the Clausius theorem, this definition has been derived from a three-level model system. As previously shown in our study of a two-level system, introduction of an additional parameter, i.e. an internal temperature, is useful to describe the relation between energy and entropy changes in non-equilibrium states. Because a further extension is indispensable to deal with more realistic glass models, we define here temperature as a tensor whose diagonal components, the statistical temperatures, constitute a bridge between thermodynamic variables and a partition function in the framework of non-equilibrium statistical mechanics. On the other hand, the non-diagonal components, named thermodynamic temperatures, are used to extend the Clausius theorem within the framework of non-equilibrium thermodynamics. The new formalism is applied to a three-level model as the simplest example of multilevel system. It succeeds in describing the relation between energy changes and entropy in non-equilibrium states. In addition, this study sheds a new light on the interpretation of the second law of thermodynamics. As a result, Clausius' definition of entropy, and its famous inequality for non-equilibrium cases can be merged into a single equality without the introduction of any additional terms. In addition, this study introduces a more general definition of the zeroth law of thermodynamics for non-equilibrium conditions, and extends the concept of fictive temperature as an order parameter to distinguish non-equilibrium glasses.
- Subjects
NONEQUILIBRIUM statistical mechanics; NONEQUILIBRIUM thermodynamics; THERMODYNAMICS; STATISTICAL thermodynamics; STATISTICAL mechanics; SECOND law of thermodynamics; THERMODYNAMIC laws
- Publication
Physics & Chemistry of Glasses: European Journal of Glass Science & Technology Part B, 2021, Vol 62, Issue 1, p8
- ISSN
1753-3562
- Publication type
Article
- DOI
10.13036/17533562.62.1.011