Structural Viscosity, Thermal Waves, and the Mpemba Effect from Extended Structural Dynamics

TL;DR

This paper introduces Extended Structural Dynamics (ESD), a kinetic framework that models finite-speed thermal and momentum transport phenomena, providing new insights into anisotropic transport, shock regularization, and the Mpemba effect.

Contribution

It develops a novel hyperbolic transport theory from an extended Boltzmann equation, capturing finite propagation speeds and anisotropic effects in fluids with extended constituents.

Findings

Predicts finite thermal and momentum wave speeds.

Derives a kinetic basis for micropolar fluid theory.

Estimates structural effects can dominate classical transport coefficients.

Abstract

Classical hydrodynamics rests on the point-particle idealization, leading to parabolic transport equations, infinite signal speeds, and the inability to capture finite time relaxation, anisotropic transport, or non Fourier thermal phenomena. This work introduces Extended Structural Dynamics (ESD), a kinetic framework in which constituents are described as spatially extended objects possessing orientation, angular momentum, and internal deformation modes. Starting from an extended Boltzmann equation, a Chapman Enskog expansion with BGK closure yields two hyperbolic parabolic transport laws: a dynamical spin equation coupling orientational relaxation to fluid vorticity, and a heat flux relaxation equation with structural thermal conductivity. These equations predict finite propagation speeds for momentum and heat, intrinsic shock regularization, anisotropic transport, and thermal waves. The spin equation provides a kinetic derivation of micropolar fluid theory, while the heat flux equation supplies a microscopic foundation for Cattaneo Vernotte behavior. Quantitative estimates indicate structural contributions can dominate classical transport coefficients. The BGK closure preserves the qualitative geometric structure of extended phase space and captures correct scaling; the connection between the orientational relaxation time and Lyapunov instability is established independently. The resulting scaling laws follow from rotational-translational coupling. Predictions include Mpemba crossover time for colloidal ellipsoids and shock width for asymmetric molecules, both testable with existing techniques.