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Many analyses based on the time-dependent Ginzburg--Landau model are notconsistent with statistical mechanics, because thermal fluctuations are nottaken correctly into account. We use the fluctuation-dissipation theorem inorder to establish the appropriate size of the Langevin terms, and thus ensurethe required consistency. Fluctuations of the electromagnetic potential areessential, even when we evaluate quantities that do not depend directly on it.Our method can be cast in gauge-invariant form. We perform numerous tests, andall the results are in agreement with statistical mechanics. We apply ourmethod to evaluate paraconductivity of a superconducting wire. TheAslamazov--Larkin result is recovered as a limiting situation. Our method isnumerically stable and the nonlinear term is easily included. We attempt acomparison between our numerical results and the available experimental data.Within an appropriate range of currents, phase slips occur, but we found noevidence for thermally activated phase slips. We studied the behavior of amoderate constriction. A constriction pins and enhances the occurrence of phaseslips.Comment: contains new sections that deal with phase slip

Ginzburg-Landau equations with consistent Langevin terms for nonuniform wires