Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Time-symmetric Microscopic Dynamics to Time-asymmetric Macroscopic
  Behavior: An Overview   Time-asymmetric behavior as embodied in the second law of thermodynamics is
observed in {\it individual macroscopic} systems. It can be understood as
arising naturally from time-symmetric microscopic laws when account is taken of
a) the great disparity between microscopic and macroscopic scales, b) a low
entropy state of the early universe, and c) the fact that what we observe is
the behavior of systems coming from such an initial state--not all possible
systems. The explanation of the origin of the second law based on these
ingredients goes back to Maxwell, Thomson and particularly Boltzmann. Common
alternate explanations, such as those based on the ergodic or mixing properties
of probability distributions (ensembles) already present for chaotic dynamical
systems having only a few degrees of freedom or on the impossibility of having
a truly isolated system, are either unnecessary, misguided or misleading.
Specific features of macroscopic evolution, such as the diffusion equation, do
however depend on the dynamical instability (deterministic chaos) of
trajectories of isolated macroscopic systems.
  The extensions of these classical notions to the quantum world is in many
ways fairly direct. It does however also bring in some new problems. These will
be discussed but not resolved.

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The categories of this paper are: math
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin