G. Bianconi: Gravity from Entropy

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SUMMARY

The discussion focuses on the papers by Prof. G. Bianconi, specifically "Gravity from Entropy" and "Quantum entropy couples matter with geometry." The first paper presents a Lorentzian spacetime framework, while the second explores discrete spacetime through higher-order networks. Both papers utilize an entropy-based variational principle, linking gravitational dynamics to quantum relative entropy between metrics influenced by matter fields. The formalism effectively recovers key equations such as the Einstein equations, Klein-Gordon, and Dirac equations in their respective limits.

PREREQUISITES
  • Understanding of Lorentzian spacetime concepts
  • Familiarity with higher-order networks in discrete spacetime
  • Knowledge of entropy-based variational principles
  • Basic grasp of differential geometry and field theory
NEXT STEPS
  • Study the implications of entropy in gravitational dynamics
  • Explore the applications of higher-order networks in physics
  • Investigate the derivation of Einstein equations from variational principles
  • Learn about the relationship between quantum mechanics and spacetime geometry
USEFUL FOR

Physicists, researchers in theoretical physics, and students interested in the intersection of quantum mechanics and general relativity will benefit from this discussion.

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antaris said:
So as I read correct the first paper describes an lorentzian spacetime and the second describes an discrete spacetime from higher order networks.

Both documents use an entropy–based variational principle in which the gravitational dynamics
(or network geometry dynamics in the discrete case) arise from a quantum relative entropy
between a default (or bare) metric and an induced metric determined by matter (and gauge)
fields. The continuum version formulates these ideas in the language of differential geometry and
field theory, while the discrete version adapts them to the combinatorial and algebraic setting
of higher–order networks. In both cases the formalism is consistent and the derived equations
(Einstein equations, Klein–Gordon and Dirac equations) are recovered in appropriate limits.

The discrete version leads to the Dirac- and Klein-Gordon-Equotation and the continuum version leads to macroscopic spacetime of the RT. Is this right?
 
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