Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the
  Absence of Detailed Balance. II: construction of SDS with nonlinear force and
  multiplicative noise   There is a whole range of emergent phenomena in non-equilibrium behaviors can
be well described by a set of stochastic differential equations. Inspired by an
insight gained during our study of robustness and stability in phage lambda
genetic switch in modern biology, we found that there exists a classification
of generic nonequilibrium processes: In the continuous description in terms of
stochastic differential equations, there exists four dynamical elements: the
potential function $\phi$, the friction matrix $ S$, the anti-symmetric matrix
$ T $, and the noise. The generic feature of absence of detailed balance is
then precisely represented by $T$. For dynamical near a fixed point, whether or
not it is stable or not, the stochastic dynamics is linear. A rather complete
analysis has been carried out (Kwon, Ao, Thouless, cond-mat/0506280; PNAS, {\bf
102} (2005) 13029), referred to as SDS I. One important and persistent question
is the existence of a potential function with nonlinear force and with
multiplicative noise, with both nice local dynamical and global steady state
properties. Here we demonstrate that a dynamical structure built into
stochastic differential equation allows us to construct such a global
optimization potential function. First, we provide the construction. One of
most important ingredient is the generalized Einstein relation. We then present
an approximation scheme: The gradient expansion which turns every order into
linear matrix equations. The consistent of such methodology with other known
stochastic treatments will be discussed in next paper, SDS III; and the
explicitly connection to statistical mechanics and thermodynamics will be
discussed in a forthcoming paper, SDS IV.

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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn