# Classical and quantum geometric information flows and entanglement of relativistic mechanical systems

@article{Vacaru2019ClassicalAQ, title={Classical and quantum geometric information flows and entanglement of relativistic mechanical systems}, author={Sergiu I. Vacaru and Laurenctiu Bubuianu}, journal={Quantum Inf. Process.}, year={2019}, volume={18}, pages={376} }

This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigory Perelman's entropy for geometric flows and associated statistical…

## 5 Citations

### Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems

- Physics
- 2019

This work consists an introduction to the classical and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. Basic geometric and physical properties…

### Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies

- MathematicsQuantum Inf. Process.
- 2022

We investigate classical and quantum geometric information flow theories (GIFs and QGIFs) when the geometric flow evolution and field equations for nonholonomic Einstein systems, NES, are derived…

### Kaluza–Klein gravity and cosmology emerging from G. Perelman’s entropy functionals and quantum geometric information flows

- Physics
- 2021

We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein–Maxwell and Kaluza–Klein, KK, theories formulated in Lagrange–Hamilton and general covariant variables.…

### Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions

- PhysicsThe European Physical Journal Plus
- 2020

We elaborate on statistical thermodynamics models of relativistic geometric flows as generalisations of G. Perelman and R. Hamilton theory centred around C. Caratheodory axiomatic approach to…

## References

SHOWING 1-10 OF 74 REFERENCES

### Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems

- Physics
- 2019

This work consists an introduction to the classical and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. Basic geometric and physical properties…

### Entanglement in quantum critical phenomena.

- PhysicsPhysical review letters
- 2003

The results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories.

### Entanglement Entropy from Numerical Holography

- Physics
- 2018

In this thesis I present numerical studies of entanglement entropy and the quantum null energy condition in strongly coupled far-from-equilibrium quantum states using holography. I give a careful…

### The role of relative entropy in quantum information theory

- Physics
- 2002

Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are…

### Entanglement Entropy of Black Holes

- PhysicsLiving reviews in relativity
- 2011

The focus in the review is on the systematic use of the conical singularity method and the puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, which is illustrated on two- and four-dimensional examples.

### Exact solutions for E. Verlinde emergent gravity and generalized G. Perelman entropy for geometric flows

- Physics
- 2019

We develop an approach to the theory of relativistic geometric flows and emergent gravity defined by entropy functionals and related statistical/geometric thermodynamics models. There are considered…

### Measuring Gaussian quantum information and correlations using the Rényi entropy of order 2.

- Computer Science, PhysicsPhysical review letters
- 2012

We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon…

### Area laws in quantum systems: mutual information and correlations.

- PhysicsPhysical review letters
- 2008

This Letter shows that the holographic principle not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law.

### Entanglement Renormalization and Holography

- Physics
- 2012

We show how recent progress in real space renormalization group methods can be used to define a generalized notion of holography inspired by holographic dualities in quantum gravity. The…

### Topological entanglement entropy.

- PhysicsPhysical review letters
- 2006

The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity.