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Entropy 2018, 20(3), 149; https://doi.org/10.3390/e20030149

Hierarchy of Relaxation Times and Residual Entropy: A Nonequilibrium Approach

1
Department of Physics, The University of Akron, Akron, OH 44325, USA
2
Department of Polymer Science, The University of Akron, Akron, OH 44325, USA
Received: 29 January 2018 / Revised: 21 February 2018 / Accepted: 22 February 2018 / Published: 26 February 2018
(This article belongs to the Special Issue Residual Entropy and Nonequilibrium States)
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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 τ obs , 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 T ( t ) and the pressure P ( t ) of the system, which deviate from their external values. View Full-Text
Keywords: relaxation hierarchy; residual entropy; nonequilibrium thermodynamics; internal variables; hierarchy of state spaces; tool-narayanaswamy equation; entropy bound relaxation hierarchy; residual entropy; nonequilibrium thermodynamics; internal variables; hierarchy of state spaces; tool-narayanaswamy equation; entropy bound
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Gujrati, P.D. Hierarchy of Relaxation Times and Residual Entropy: A Nonequilibrium Approach. Entropy 2018, 20, 149.

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