A unified theory of free energy functionals and applications to diffusion Article Swipe
Andrew B. Li
,
Leonid Miroshnik
,
Brian Rummel
,
Ganesh Balakrishnan
,
Sang M. Han
,
Talid Sinno
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1073/pnas.2203399119
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1073/pnas.2203399119
Free energy functionals of the Ginzburg–Landau type lie at the heart of a broad class of continuum dynamical models, such as the Cahn–Hilliard and Swift–Hohenberg equations. Despite the wide use of such models, the assumptions embodied in the free energy functionals frequently either are poorly justified or lead to physically opaque parameters. Here, we introduce a mathematically rigorous pathway for constructing free energy functionals that generalizes beyond the constraints of Ginzburg–Landau gradient expansions. We show that the formalism unifies existing free energetic descriptions under a single umbrella by establishing the criteria under which the generalized free energy reduces to gradient-based representations. Consequently, we derive a precise physical interpretation of the gradient energy parameter in the Cahn–Hilliard model as the product of an interaction length scale and the free energy curvature. The practical impact of our approach is demonstrated using both a model free energy function and the silicon–germanium alloy system.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1073/pnas.2203399119
- OA Status
- green
- Cited By
- 1
- References
- 57
- Related Works
- 10
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W4225645756Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1073/pnas.2203399119Digital Object Identifier
- Title
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A unified theory of free energy functionals and applications to diffusionWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-06-01Full publication date if available
- Authors
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Andrew B. Li, Leonid Miroshnik, Brian Rummel, Ganesh Balakrishnan, Sang M. Han, Talid SinnoList of authors in order
- Landing page
-
https://doi.org/10.1073/pnas.2203399119Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2203.06813Direct OA link when available
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1Total citation count in OpenAlex
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2025: 1Per-year citation counts (last 5 years)
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57Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| referenced_works | https://openalex.org/W2066359652, https://openalex.org/W2085956855, https://openalex.org/W2966735816, https://openalex.org/W2951753406, https://openalex.org/W2895707213, https://openalex.org/W2794917763, https://openalex.org/W3019152834, https://openalex.org/W2097973750, https://openalex.org/W2990233693, https://openalex.org/W3030510149, https://openalex.org/W2785804197, https://openalex.org/W4205893973, https://openalex.org/W2058607346, https://openalex.org/W1987066247, https://openalex.org/W2745254744, https://openalex.org/W2586427664, https://openalex.org/W2788652239, https://openalex.org/W3084496242, https://openalex.org/W2001222525, https://openalex.org/W3021128674, https://openalex.org/W2046528357, https://openalex.org/W2077517062, https://openalex.org/W2011740867, https://openalex.org/W1966096451, https://openalex.org/W2964801260, https://openalex.org/W1990527824, https://openalex.org/W2049754553, https://openalex.org/W4236525788, https://openalex.org/W1997312491, https://openalex.org/W3016412753, https://openalex.org/W2266688862, https://openalex.org/W2901149131, https://openalex.org/W2920702560, https://openalex.org/W2966563252, https://openalex.org/W2039016663, https://openalex.org/W1971593804, https://openalex.org/W2161863039, https://openalex.org/W2051497316, https://openalex.org/W1982312043, https://openalex.org/W1993059698, https://openalex.org/W1975429982, https://openalex.org/W2055792303, https://openalex.org/W1643519861, https://openalex.org/W2569713119, https://openalex.org/W1994402496, https://openalex.org/W2052031259, https://openalex.org/W2912164969, https://openalex.org/W2021311319, https://openalex.org/W1548256084, https://openalex.org/W2089221899, https://openalex.org/W2588826488, https://openalex.org/W2806280421, https://openalex.org/W2056546053, https://openalex.org/W2000883601, https://openalex.org/W2901995873, https://openalex.org/W2994626356, https://openalex.org/W3049695724 |
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