Coherence as Thermodynamic Organization: Toward a Non-Equilibrium Turbulence Theory

Abstract

Since the foundational studies in the late nineteenth century, fluid turbulence has stood as a profound, unsolved challenge in classical physics. Much of this enduring difficulty stems from non-equilibrium turbulence, where the lack of a unifying physical framework for macroscopic coherent structures has hampered predictive flow modeling. Here, we establish a foundational bridge between non-equilibrium statistical physics and turbulent coherent structures through the renormalized Navier-Stokes equations. We demonstrate that all forms of turbulent coherence are fundamentally universal thermodynamic responses mandated by macroscopic energy throughput imbalances. Depending on topological access to bifurcations, these formations manifest either as transient adjustments (analogous to Kubo's near-equilibrium fluctuations) or as autonomous, transformative states (mirroring Prigogine's far-from-equilibrium dissipative structures). By introducing a computable, effective thermodynamic order parameter ($Π$), this paradigm establishes a rigorous foundation for non-equilibrium theory, enabling unequivocal identification of necessary flow resolution in continuously driven, dissipative continuum systems.