Fractional Nonholonomic Ricci Flows

TL;DR

This paper develops a fractional Ricci flow theory for nonholonomic (pseudo) Riemannian geometries with non-integer dimensions, introducing fractional analogs of Perelman's functionals and evolution equations, with applications to gravity and thermodynamics.

Contribution

It introduces a novel fractional Ricci flow framework for nonholonomic geometries, extending classical geometric analysis to fractional and non-integer dimensional settings.

Findings

Constructed fractional analogs of Perelman's functionals.

Derived fractional Ricci flow (Hamilton's) equations.

Analyzed fractional operators for entropy and thermodynamics.

Abstract

We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman's functionals and derived the corresponding fractional evolution (Hamilton's) equations. We apply in fractional calculus the nonlinear connection formalism originally elaborated in Finsler geometry and generalizations and recently applied to classical and quantum gravity theories. There are also analyzed the fractional operators for the entropy and fundamental thermodynamic values.