Onsager Vacuum: Driven-Dissipative Non-Equilibrium Statistical Mechanics of the Vorton Cascade

The monograph establishes a closed, three-stage non-equilibrium steady state that bridges continuous runaway vortex dynamics with linear transport on a discrete vacuum lattice: Breakdown of Classical 3D Equilibrium: Unlike two-dimensional point-vortex systems, three-dimensional unconstrained vortex dipole gases possess no conserved Hamiltonian or classical hydrodynamic invariants. Instead of thermalizing in a microcanonical ensemble, the gas undergoes finite-time intensity blowup and phase-space evacuation governed by cubic space-time scaling. The Orthogonal-Triad Attractor: Approaching the singularity, dominant vortex pairs self-organize into a mutually perpendicular geometry where their circulation vectors and separation line are mutually orthogonal. This state does not maximize instantaneous two-body growth, but acts as a collective, many-body chiral attractor sustained by background turbulent strain. Singular Reconnection Sink: The continuous blowup terminates at the microscopic core scale via topological reconnection. This event halts runaway growth and converts continuous convective dissipation into discrete quantized packets of circulation, linking charge, enstrophy, and link energy. Network Relaxation Substrate: Ejected quanta relax across an 861-node discrete network. The network's spectral gap and effective resistance strictly bound the maximum irreversible dissipation delay of injected topological perturbations. Reciprocity and Topological Transport: Because the transported densities are even under microscopic time reversal, the macroscopic linear transport matrix is purely symmetric, with no antisymmetric corrections. Enstrophy gradients deterministically drive quantized linking currents through a Topological Seebeck Effect, governed by discrete Poisson fluctuation relations and an exact Fano factor.