Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical Evolution in Noncommutative Discrete Phase Space and the
  Derivation of Classical Kinetic Equations   By considering a lattice model of extended phase space, and using techniques
of noncommutative differential geometry, we are led to: (a) the conception of
vector fields as generators of motion and transition probability distributions
on the lattice; (b) the emergence of the time direction on the basis of the
encoding of probabilities in the lattice structure; (c) the general
prescription for the observables' evolution in analogy with classical dynamics.
We show that, in the limit of a continuous description, these results lead to
the time evolution of observables in terms of (the adjoint of) generalized
Fokker-Planck equations having: (1) a diffusion coefficient given by the limit
of the correlation matrix of the lattice coordinates with respect to the
probability distribution associated with the generator of motion; (2) a drift
term given by the microscopic average of the dynamical equations in the present
context. These results are applied to 1D and 2D problems. Specifically, we
derive: (I) The equations of diffusion, Smoluchowski and Fokker-Planck in
velocity space, thus indicating the way random walk models are incorporated in
the present context; (II) Kramers' equation, by further assuming that, motion
is deterministic in coordinate space

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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex