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We study dissipation in inhomogeneous two-dimensional electron systems. Wepredict a relatively strong current-induced spatial asymmetry in the heating ofthe electron and phonon systems -- even if the inhomogeneity responsible forthe electrical resistance is symmetric with respect to the current direction.We also show that the heat distributions in the hydrodynamic andimpurity-dominated limits are essentially different. In particular, within awide, experimentally relevant interval of driving fields, the dissipationprofile in the hydrodynamic limit turns out to be asymmetric, and thecharacteristic spatial scale of the temperature distribution can be controlledby the driving field. By contrast, in the same range of parameters,impurity-dominated heating is almost symmetric, with the size of thedissipation region being independent of the field. This allows one todistinguish experimentally the hydrodynamic and impurity-dominated limits. Ourresults are consistent with recent experimental findings on transport anddissipation in narrow constrictions and quantum point contacts.

Asymmetry of non-local dissipation: From drift-diffusion to hydrodynamics