Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irreversible Circulation of Fluctuation and Entropy Production   Physical and chemical stochastic processes described by the master equation
are investigated. In this paper, we examine the entropy production both for the
master equation and for the corresponding Fokker-Planck equation. For the
master equation, the exact expression of the entropy production was recently
derived by Gaspard using the Kolmogorov-Sinai entropy ({\em J.Stat.Phys.},
\textbf{117} (2004), 599; [Errata; \textbf{126} (2006), 1109 ]). Although
Gaspard's expression is derived from a stochastic consideration, it should be
noted that Gaspard's expression conincides with the thermodynamical expression.
For the corresponding Fokker-Planck equation, by using the detailed imbalance
relation which appears in the derivation process of the fluctuation theorem
through the Onsger-Machlup theory, the entropy production is expressed in terms
of the {\em irreversible circulation of fluctuation}, which was proposed by
Tomita and Tomita ({\em Prog.Theor.Phys.}, \textbf{51} (1974), 1731). However,
this expression for the corresponding Fokker-Planck equation differs from that
of the entropy production for the master equation. This discrepancy is due to
the difference between the master equation and the corresponding Fokker-Planck
equation, namely the former treats discrete events, but the latter equation is
an approximation of the former one. In fact, in the latter equation, the
original discrete events are smoothed out. To overcome this difficulty, we
propose the {\em path weight principle}. By using this principle, the modified
expression of the entropy production for the corresponding Fokker-Planck
equation coincides with that of the master equation (i.e., the thermodynamical
expression) for a simple chemical reaction system and a diffusion system.

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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas