  We geometrically characterize one-qubit dissipators of a Lindblad type. An
efficient parametrization in terms of 6 linear parameters opens the way to
various optimizations with local dissipation. As an example, we study maximal
steady-state singlet fraction that can be achieved with an arbitrary local
dissipation and two qubit Hamiltonian. We show that this singlet fraction has a
discontinuity as one moves from unital to non-unital dissipators and
demonstrate that the largest possible singlet fraction is approximately 0.654.
This means that for systems with a sufficiently entangled ground state there is
a fundamental quantum limit to the lowest attainable energy. With local
dissipation one is unable to cool the system below some limiting non-zero
temperature.
