A non equilibrium Ising model of turbulence

TL;DR

This paper presents a novel non-equilibrium Ising model of turbulence that captures phase transition signatures and distinguishes between near-equilibrium and turbulent regimes, useful for studying out-of-equilibrium turbulence.

Contribution

It introduces a multi-resolution lattice model driven by Ising dynamics that bridges equilibrium phase transitions and turbulent out-of-equilibrium states.

Findings

Model retains equilibrium phase transition signatures.

Critical temperature aligns with maximum entropy state.

Distinguishes regimes satisfying Onsager relations and turbulent states.

Abstract

We introduce a model of interacting lattices at different resolutions driven by the two-dimensional Ising dynamics with a nearest-neighbor interaction. We study this model both with tools borrowed from equilibrium statistical mechanics as well as non-equilibrium thermodynamics. Our findings show that this model keeps the signature of the equilibrium phase transition. Moreover the critical temperature of the equilibrium models correspond to the state maximizing the entropy and delimits two out-of-equilibrium regimes, one satisfying the Onsager relations for systems close to equilibrium and one resembling convective turbulent states. Since the model preserves the entropy and energy fluxes in the scale space, it seems a good candidate for parametric studies of out-of-equilibrium turbulent systems.