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Complex network growth model: Possible isomorphism between nonextensive statistical mechanics and random geometry.

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This study reveals a new connection between statistical mechanics and random geometry. It identifies an isomorphism linking a specific q-exponential distribution to a geographic growth model, expanding known relationships in physics.

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Area of Science:

  • Statistical Mechanics and Random Geometry
  • Non-additive Entropy and Complex Systems

Background:

  • Established isomorphisms link statistical mechanics models (Potts ferromagnet, n-vector ferromagnet) to random geometry concepts (bond percolation, random resistor networks, self-avoiding walks).
  • These connections are crucial for understanding complex systems and emergent behaviors in physics.

Purpose of the Study:

  • To explore and provide numerical evidence for a novel isomorphism in statistical mechanics.
  • To connect the energy q-exponential distribution (q=4/3) with a geographic growth random model.

Main Methods:

  • Numerical simulations were employed to investigate the proposed isomorphism.
  • The study focused on the optimization of nonadditive entropy (S) under simple constraints.
  • Analysis involved a geographic growth random model with preferential attachment and exponentially distributed weighted links.

Main Results:

  • Strong numerical evidence suggests a new isomorphism exists.
  • This isomorphism links the q-exponential distribution (q=4/3, βω=10/3) to a specific geographic growth model.
  • The model utilizes preferential attachment with exponentially distributed weights (ω).

Conclusions:

  • A novel connection between nonadditive entropy optimization and random geometric growth models has been identified.
  • This finding extends the known isomorphisms in statistical mechanics, offering new avenues for research in complex systems and network theory.