Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Theory of Free Energy Functionals and Applications to
  Diffusion   Free energy functionals of 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 are frequently either 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
new 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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The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg