The dynamic of moving vortex matter is considered in the framework of the time dependent Ginzburg - Landau equation beyond linear response. Both disorder and thermal fluctuations are included using the Martin-Siggia-Rose formalism within the lowest Landau level approximation. We determine the critical current as function of magnetic field and temperature. The surface in the J-B-T space defined by the function separates between the dissipative moving vortex matter regime (qualitatively appearing as either the vortex creep and flux flow) and dissipation less current state in which vortices are pinned creating an amorphous vortex "glass". Both the thermal depinning and the depinning by a driving force are taken into account. The static irreversibility line is compared to experiments and is consistent with the one obtained in the replica approach. The non-Ohmic I-V curve (in the depinned phase) is obtained and resistivity compared with experiments in layered superconductors and thin films.