2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/16920The dual 'worldline', or 'string', description of adiabatic Ginzburg-Landau field theory near a phase transition in terms of quasi-Brownian strings and loops is well understood. In reality, the implementation of a transition is intrinsically non-equilibrium. We sketch how time-dependent Ginzburg-Landau theory leads to a modified dual string picture in which a causal bound on the growth of unstable string prevents the uncontrolled proliferation of string (the Shockley-Hagedorn transition) suggested by the adiabatic approximation.4 pages Revtex, no figuresCondensed MatterHigh Energy Physics - Theorytext