Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative
  Ricci Flows   We formulate a noncommutative generalization of the Ricci flow theory in the
framework of spectral action approach to noncommutative geometry. Grisha
Perelman's functionals are generated as commutative versions of certain
spectral functionals defined by nonholonomic Dirac operators and corresponding
spectral triples. We derive the formulas for spectral averaged energy and
entropy functionals and state the conditions when such values describe
(non)holonomic Riemannian configurations.

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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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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: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex