Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Stochastic Dynamics of Complex Systems, I: A Chemical Reaction
  Kinetic Perspective with Mesoscopic Nonequilibrium Thermodynamics   We distinguish a mechanical representation of the world in terms of point
masses with positions and momenta and the chemical representation of the world
in terms of populations of different individuals, each with intrinsic
stochasticity, but population wise with statistical rate laws in their
syntheses, degradations, spatial diffusion, individual state transitions, and
interactions. Such a formal kinetic system in a small volume $V$, like a single
cell, can be rigorously treated in terms of a Markov process describing its
nonlinear kinetics as well as nonequilibrium thermodynamics at a mesoscopic
scale. We introduce notions such as open, driven chemical systems, entropy
production, free energy dissipation, etc. Then in the macroscopic limit, we
illustrate how two new "laws", in terms of a generalized free energy of the
mesoscopic stochastic dynamics, emerge. Detailed balance and complex balance
are two special classes of "simple" nonlinear kinetics. Phase transition is
intrinsically related to multi-stability and saddle-node bifurcation
phenomenon, in the limits of time $t\rightarrow\infty$ and system's size
$V\rightarrow\infty$. Using this approach, we re-articulate the notion of
inanimate equilibrium branch of a system and nonequilibrium state of a living
matter, as originally proposed by Nicolis and Prigogine, and seek a logic
consistency between this viewpoint and that of P. W. Anderson and J. J.
Hopfield's in which macroscopic law emerges through symmetry breaking.

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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
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The categories of this paper are: q-alg
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: stat