Energy Gap Model of Glass Formers: Lessons Learned from Polymers

Gujrati, P. D.

doi:10.1002/9783527630257.ch10

Cited by 7 publications

(14 citation statements)

References 109 publications

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“…We have concluded in previous work [52,58] that temporal averages may not be relevant at low temperatures where component confinement occurs in of thermodynamically significant several disjoined components. The glass is formed when the system gets trapped in one of these components.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Compared to the glass, the supercooled liquid (SCL) is in constrained equilibrium [70,71], and its entropy is shown by the continuous curve in Figure 4). Over the glass transition region between T 0G and T 0g , the nonequilibrium liquid (dotted curve) gradually turns from SCL at or above T 0g into a glass at or below T 0G [58]. Over this region, thermodynamic quantities such as the volume or the enthalpy change continuously but slowly during cooling.…”

Section: Vitrification and The Residual Entropymentioning

confidence: 99%

“…As dynamics is very fast here, it is well known that the ensemble entropy agrees with its temporal formulation. However, at low temperatures, where dynamics becomes sluggish as in a glass [57,58], the system can be confined into disjoint components. This occurs when the observational time scale τ obs becomes shorter than the equilibration time τ eq ; see also Section 4.…”

Section: Statistical Entropy With Component Confinementmentioning

confidence: 99%

“…Using a non-trivial example, we demonstrate how it emerges from a non-negative statistical entropy. The third hurdle we encounter is with Boltzmann's concept of the number of microstates when dealing with systems such as glasses [57,58] where we encounter component confinement over a long period of time; see footnote 10 and Section 7. Component confinement occurs at low temperatures where equilibration time τ eq becomes larger than the observation or measurement time τ obs .…”

Section: Macroscopic System T(t) P(t)mentioning

confidence: 99%

See 3 more Smart Citations

On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies

Gujrati

2015

Entropy

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Abstract:We review the concept of nonequilibrium thermodynamic entropy and observables and internal variables as state variables, introduced recently by us, and provide a simple first principle derivation of additive statistical entropy, applicable to all nonequilibrium states by treating thermodynamics as an experimental science. We establish their numerical equivalence in several cases, which includes the most important case when the thermodynamic entropy is a state function. We discuss various interesting aspects of the two entropies and show that the number of microstates in the Boltzmann entropy includes all possible microstates of non-zero probabilities even if the system is trapped in a disjoint component of the microstate space. We show that negative thermodynamic entropy can appear from nonnegative statistical entropy.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Vitrification and The Residual Entropymentioning

confidence: 99%

Section: Statistical Entropy With Component Confinementmentioning

confidence: 99%

Section: Macroscopic System T(t) P(t)mentioning

confidence: 99%

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On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies

Gujrati

2015

Entropy

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“…As the dynamics is very fast here, it is well known that the ensemble averages agree with temporal averages. However, at low temperatures, where dynamics becomes sluggish as in a glass [ 3 , 33 , 34 , 35 ], the system can be confined into disjoint components. The confinement occurs under NEQ conditions, when the observational time scale

becomes shorter than the equilibration time

, such as in glasses, whose behavior and properties have been extensively studied.…”

Section: Introductionmentioning

confidence: 99%

Hierarchy of Relaxation Times and Residual Entropy: A Nonequilibrium Approach

Gujrati

2018

Entropy

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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.

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The Glass Transition and the Entropy Crisis

Gujrati

2021

Encyclopedia of Glass Science, Technology, History, and Culture

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Energy Gap Model of Glass Formers: Lessons Learned from Polymers

Cited by 7 publications

References 109 publications

On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies

On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies

Hierarchy of Relaxation Times and Residual Entropy: A Nonequilibrium Approach

The Glass Transition and the Entropy Crisis

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