We study the hydrodynamics of superconductors within framework Schwinger-Keldysh Effective Field Theory. show that in vicinity superconducting phase transition most general leading-order EFT satisfying local Kubo-Martin-Schwinger condition is described by a version Time-Dependent Ginzburg-Landau (TDGL) equations augmented with stochastic terms. This TDGL applicable gapless regime independently ...