Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

Bubuianu, Iuliana; Vacaru, Sergiu I.; Veliev, E. Veli

doi:10.1016/j.aop.2020.168333

Cited by 9 publications

(91 citation statements)

References 91 publications

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“…In letter [32], we shown that models of entropic gravity can be derived from nonholonomic modifications of the Wfunctional when the (modified) Einstein equations are equivalent to certain nonholonomic Ricci soliton equations. Here, we shall study the conditions when entropic elastic scenarios can be modelled as nonholonomic Ricci solitons in Sect.…”

Section: Distributions Defining Spacetime Elastic Configurationsmentioning

confidence: 99%

“…3.3. We shall consider certain examples of nonholonomic distributions and related Lagrange densities on a Lorentz manifold V which are used in entropic gravity theories [6,7,32,65]. Using such geometric constructions, we shall elaborate in next section on elastic flow evolution models and their selfsimilar nonholonomic Ricci soliton configurations.…”

Section: Distributions Defining Spacetime Elastic Configurationsmentioning

confidence: 99%

“…It was proposed that such a phenomenon occurs in the dS space being responsible for the presence of a cosmological horizon. Nevertheless, in this series of two works, see [32] as a partner paper with complementary results, we deal with quite different issues on geometric flow modifications of gravity and spacetime thermodynamics. It is just shown that relativistic generalizations with a corresponding choice of evolution and thermodynamic functionals support the ideas on the origin of gravity as an effect of the entropic force but with a new type of geometric thermodynamics entropy.…”

Section: Introductionmentioning

confidence: 99%

“…Three lines of evidence motivate this article and the partner letter [32]. First, we use our former results and nonholonomic geometric methods [33][34][35][36][37][38][39][40][41] that generalized/modified relativistic flow equations and Einstein equations in GR and MGTs can be derived as systems of PDEs for modified Ricci solitons for respective nonholonomic modifications of G. Perelman's F-and W-entropy functionals.…”

Section: Introductionmentioning

confidence: 99%

“…In Sect. 4, we develop and apply the anholonomic frame deformation method, AFDM, [32,38,40,58,63,64] in order to prove general decoupling properties and integrability of nonholonomic geometric flow and Ricci soliton equations encoding elastic and quasiperiodic spacetime and (effective) matter fields properties. Such solutions are described by generic off-diagonal metrics, and generalized connections, depending on all spacetime coordinates and temperature like parameters via general classes of generating functions and (effective) sources of entropic gravity and matter fields.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

Vacaru

Veliev

Bubuianu³

2021

Eur. Phys. J. C

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We develop an approach to the theory of relativistic geometric flows and emergent gravity defined by entropy functionals and related statistical thermodynamics models. Nonholonomic deformations of G. Perelman’s functionals and related entropic values used for deriving relativistic geometric evolution flow equations. For self-similar configurations, such equations describe generalized Ricci solitons defining modified Einstein equations. We analyse possible connections between relativistic models of nonholonomic Ricci flows and emergent modified gravity theories. We prove that corresponding systems of nonlinear partial differential equations, PDEs, for entropic flows and modified gravity posses certain general decoupling and integration properties. There are constructed new classes of exact and parametric solutions for nonstationary configurations and locally anisotropic cosmological metrics in modified gravity theories and general relativity. Such solutions describe scenarios of nonlinear geometric evolution and gravitational and matter field dynamics with pattern-forming and quasiperiodic structure and various space quasicrystal and deformed spacetime crystal models. We analyse new classes of generic off-diagonal solutions for entropic gravity theories and show how such solutions can be used for explaining structure formation in modern cosmology. Finally, we speculate why the approaches with Perelman–Lyapunov type functionals are more general or complementary to the constructions elaborated using the concept of Bekenstein–Hawking entropy.

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Section: Distributions Defining Spacetime Elastic Configurationsmentioning

confidence: 99%

Section: Distributions Defining Spacetime Elastic Configurationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

Vacaru

Veliev

Bubuianu³

2021

Eur. Phys. J. C

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Nonassociative Geometric and Quantum Information Flows and R‐Flux Deformations of Wormhole Solutions in String Gravity

Bubuianu,

Singleton,

Vacaru

et al. 2024

Fortschritte der Physik

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This article consists of an introduction to the theory of nonassociative geometric classical and quantum information flows defined by star products with R‐flux deformations in string gravity. Corresponding nonassociative generalizations of the concepts of classical Shannon entropy, quantum von Neumann entropy, Rényi entropy are formulated. The fundamental geometric and quantum information objects are computed following the Grigori Perelman statistical thermodynamic approach to Ricci flows and gravity theories generalized for phase spaces modeled as (co) tangent Lorentz bundles. Nonassociative parametric deformations and nonholonomic thermo‐geometric versions of statistical generating functions, their quantum analogues as density matrices are considered for deriving the entropy, energy and fluctuation functionals. This allows us to define and compute respective classical and quantum relative and conditional entropies, mutual information and nonassociative entanglement and thermodynamic information variables. The principles of nonassociative quantum geometric and information flow theory, QGIF, and study the basic properties of such quasi‐stationary models related to modified gravity theories are formulated. Applications are considered for nonassociative deformed and entangled couples of four‐dimensional (4‐d), wormholes (defined by respective spacetime and/or momentum type coordinates) and nonassociative QGIFs of 8‐d phase space generalized wormholes configurations. Finally, phase space black holes and wormholes being transversable for nonassociative qubits, quantum channels and entanglement witness are speculated; thought and laboratory experiments are discussed; and perspectives for quantum computer modeling and tests of nonassociative geometric flow and gravity theories are considered.

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Nonassociative black holes in R-flux deformed phase spaces and relativistic models of Perelman thermodynamics

Bubuianu¹,

Singleton

Vacaru

2023

J. High Energ. Phys.

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This paper explores new classes of black hole (BH) solutions in nonassociative and noncommutative gravity, focusing on features that generalize to higher dimensions. The theories we study are modelled on (co) tangent Lorentz bundles with a star product structure determined by R-flux deformations in string theory. For the nonassociative vacuum Einstein equations we consider both real and complex effective sources. In order to analyze the nonassociative vacuum Einstein equations we develop the anholonomic frame and connection deformation methods, which allows one to decoupled and solve these equations. The metric coefficients can depend on both space-time coordinates and energy-momentum. By imposing conditions on the integration functions and effective sources we find physically important, exact solutions: (1) 6-d Tangherlini BHs, which are star product and R-flux distorted to 8-d black ellipsoids (BEs) and BHs; (2) nonassocitative space-time and co-fiber space double BH and/or BE configurations generalizing Schwarzschild-de Sitter metrics. We also investigate the concept of Bekenstein-Hawking entropy and find it applicable only for very special classes of nonassociative BHs with conventional horizons and (anti) de Sitter configurations. Finally, we show how analogs of the relativistic Perelman W-entropy and related geometric thermodynamic variables can be defined and computed for general classes of off-diagonal solutions with nonassociative R-flux deformations.

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Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

Cited by 9 publications

References 91 publications

Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

Nonassociative Geometric and Quantum Information Flows and R‐Flux Deformations of Wormhole Solutions in String Gravity

Nonassociative black holes in R-flux deformed phase spaces and relativistic models of Perelman thermodynamics

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