Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality Symmetry, Two Entropy Functions, and an Eigenvalue Problem in
  Gibbs' Theory   We generalize the convex duality symmetry in Gibbs' statistical ensemble
formulation, between Massieu's free entropy $\Phi_{V,N} (\beta)$ and the Gibbs
entropy $\varphi_{V,N}(u)$ as a function of mean internal energy $u$. The
duality tells us that Gibbs thermodynamic entropy is to the law of large
numbers (LLN) for arithmetic sample means what Shannon's information entropy is
to the LLN for empirical counting frequencies. Following the same logic, we
identify $u$ as the conjugate variable to counting frequency, a Hamilton-Jacobi
equation for Shannon entropy as an equation of state, and suggest an eigenvalue
problem for modeling statistical frequencies of correlated data.

25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex