Stability and entropy production in fractional bio-heat transport models via generalized (q, τ)-entropy
Shaher Momani, Rabha W. Ibrahim
Abstract
We propose a novel framework for modeling thermal transport in biological tissues based on a fractional bio-heat diffusion equation regularized by a generalized ( q , τ)-entropy functional. The model incorporates a Caputo-Numerical simulations demonstrate the evolution of temperature profiles and entropy dynamics, revealing the interplay between fractional memory, metabolic heat generation, and entropy-induced resistance. A stability theorem this framework offers a physically consistent and flexible approach grounded in non-equilibrium statistical mechanics and bio-thermal regulation, making it suitable for applications in complex biological media with long-range.
Topics & Concepts
Statistical physicsEntropy productionEntropy (arrow of time)Stability (learning theory)Statistical mechanicsMathematicsApplied mathematicsFractional calculusThermalHeat equationAnomalous diffusionMathematical modelPhysicsPrinciple of maximum entropyDiffusionComputer scienceDiffusion equationComplex systemContinuum mechanicsThermodynamicsStability conditionsAdvanced Thermodynamics and Statistical MechanicsFractional Differential Equations SolutionsThermoelastic and Magnetoelastic Phenomena