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