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Riemannian submersions for q-entropies

Aug 10, 2021
17 pages
Published in:
  • Int.J.Geom.Meth.Mod.Phys. 18 (2021) 14, 2150229
  • Published: Sep 25, 2021
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Abstract: (WSP)
In an attempt to find the dynamical foundations for q-entropies, we examine the special case of Lagrangian/Hamiltonian systems of many degrees of freedom whose statistical behavior is conjecturally described by the q-entropic functionals. We follow the spirit of the canonical ensemble approach. We consider the system under study as embedded in a far larger total system. We explore some of the consequences that such an embedding has, if it is modeled by a Riemannian submersion. We point out the significance in such a description of the finite-dimensional Bakry–Émery Ricci tensor, as a local mesoscopic invariant, for understanding the collective dynamical behavior of systems described by the q-entropies.
Note:
  • 17 pages. No figures, Standard LaTeX2e
  • q-entropy
  • complexity
  • submersions
  • metric-measure spaces
  • Bakry–Émery Ricci tensor
  • tensor: Ricci
  • entropy
  • collective
  • embedding
  • statistical
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