Explore the emergence of nonequilibrium steady currents in a lecture that delves into the intersection of statistical mechanics and quantum systems. Examine the scenario where two nonintegrable systems, prepared in different states, are locally and non-extensively coupled. Investigate the typical emergence of nonequilibrium quasi-steady currents for weak coupling between subsystems through perturbative analysis and numerical exact simulations of up to 28 spin systems. Discover how these currents originate from a prethermalization mechanism, involving the weak and local breaking of energy conservation for each subsystem. Progress through topics including thermalization, steady currents, current vs time analysis, and initial preparations before reaching the concluding remarks.