Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-equilibrium large deviations and parabolic-hyperbolic PDE with
  irregular drift   Large deviations of conservative interacting particle systems, such as the
zero range process, about their hydrodynamic limit and their respective rate
functions lead to the analysis of the skeleton equation; a degenerate
parabolic-hyperbolic PDE with irregular drift. We develop a robust
well-posedness theory for such PDEs in energy-critical spaces based on concepts
of renormalized solutions and the equation's kinetic form. We establish these
properties by proving that renormalized solutions are equivalent to classical
weak solutions, extending concepts of [DiPerna, Lions; Ann. Math., 1989],
[Ambrosio; Invent. Math., 2004] to the nonlinear setting.
  The relevance of the results toward large deviations in interacting particle
systems is demonstrated by applications to the identification of l.s.c.
envelopes of restricted rate functions, to zero noise large deviations for
conservative (singular) SPDE, and to the $\Gamma$-convergence of rate
functions. The first of these solves a long-standing open problem in the large
deviations for zero range processes. The second makes rigorous an informal link
between the non-equilibrium statistical mechanics approaches of macroscopic
fluctuation theory and fluctuating hydrodynamics.

10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics