Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy production in Master Equations and Fokker-Planck Equations:
  facing the coarse-graining and recovering the information loss   Systems operating out of equilibrium exchange energy and matter with the
environment, thus producing entropy in their surroundings. Since the entropy
production depends on the current flowing throughout the system, its
quantification is affected by the level of coarse-graining we adopt. In
particular, it has been shown that the description of a system via a
Fokker-Planck equation (FPE) lead to an underestimation of the entropy
production with respect to the corresponding one in terms of microscopic
transition rates. Moreover, such a correction can be derived exactly. Here we
review this derivation, generalizing it when different prescriptions to derive
the FPE from a Langevin equation are adopted. Then, some open problems about
Gaussian transition rates and underdamped limit are discussed. In the second
part of the manuscript we present a new approach to dealing with the
discrepancy in entropy production due to the coarse graining by introducing
enough microscopic variables to correctly estimate the entropy production
within the FPE description. We show that any discrete state system can be
described by making explicit the contribution of each microscopic current.

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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph