Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes about the Macroscopic Fluctuating Theory   The Macroscopic Fluctuating Theory is presented from a practical and self
consistent point of view. We take as starting point the assumption that a
system at a mesoscopic scale is described by a field $\phi(x,t)$ that evolves
by a Langevin equation that locally either conserves or not the field. Its
dynamic behavior may also depend on the action of external agents on the bulk
or/and at the system's boundaries. We derive the corresponding Fokker-Planck
equation and the probability of a path and we use them to study general
properties of the system's stationary state. In particular we focus on the
study of the quasi-potential that defines the stationary distribution at the
small noise limit. We argue that the system is at equilibrium when it is
macroscopic reversible, that is when the most probable path to create a
fluctuation from the stationary state is equal to the time reversed path that
relaxes it. When this doesn't occur the system is in a nonequilibrium
stationary state whose quasi-potential may present some lack of
differentiability and/or long range action. We also derive closed equations for
the two-body correlations at the stationary state and we apply them to some
typical cases. Finally we obtain generalized Green-Kubo class of formulas by
using the Large Deviation Principle.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org