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Abstract Kauzmann paradox (KP) suggests that deeply supercooled liquids can have a lower entropy than the corresponding crystalline solids. While this entropy catastrophe has been thoroughly studied via equilibrium thermodynamics, the solidification process occurs far‐from‐equilibrium. By analyzing this process experimentally and theoretically, we show that surface chemical speciation (oxidation‐driven generation and self‐organization of different species of the alloy components) in core‐shell particles (CSPs) can perturb the entropy production to an extent that a continuum equilibrium phase transition is not possible. Speciation of the surface causes divergence of associated stress vectors that generate nonequilibrium fluxes and frustrates homogeneous nucleation hence deep undercooling. The asymmetry of the speciation‐derived surface tensor skews the minimum entropy production criterion. We analyze a set of nonequilibrium models, one showing and one averting the entropy catastrophe. Applying thermodynamic speed limits to these models, we show that the KP takes another form. Deviations from the speed limit diverge the configurational entropy of the glass, but adding an interfacial state avoids the entropy catastrophe with significantly large supercooling.
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Foundations of a finite non-equilibrium statistical thermodynamics: extrinsic quantities
Abstract Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to conclude that statistical thermodynamics is in a state of crisis though. Indeed, the discussion about the microscopic origins of irreversibility has continued in the scientific community for more than a hundred years. This paper considers these questions while beginning to develop a statistical thermodynamics for finite non-equilibrium systems. Definitions are proposed for all of the extrinsic variables of the fundamental thermodynamic relation that are consistent with existing results in the equilibrium thermodynamic limit. The probability density function on the phase space is interpreted as a subjective uncertainty about the microstate, and the Gibbs entropy formula is modified to allow for entropy creation without introducing additional physics or modifying the phase space dynamics. Resolutions are proposed to the mixing paradox, Gibbs’ paradox, Loschmidt’s paradox, and Maxwell’s demon thought experiment. Finally, the extrinsic variables of the fundamental thermodynamic relation are evaluated as functions of time and space for a diffusing ideal gas, and the initial and final values are shown to coincide with the expected equilibrium values.
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- Award ID(s):
- 1839370
- PAR ID:
- 10392737
- Date Published:
- Journal Name:
- Journal of Physics A: Mathematical and Theoretical
- Volume:
- 55
- Issue:
- 29
- ISSN:
- 1751-8113
- Page Range / eLocation ID:
- 295002
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1751-8121/ac798a
