  The aims of this paper are two. The first is to give a brief review of the
most relevant theoretical results concerning the uniqueness of the steady-state
solution of the Lindblad-Gorini-Kossakowski-Sudarshan master equation and the
criteria which guarantee relaxingness and irreducibility of dynamical
semigroups. In particular, we test and discuss their physical meaning by
considering their applicability to the characterisation of the simplest open
quantum system \emph{i.e.} a two-level system coupled to a bath of harmonic
oscillators at zero temperature. The second aim is to provide a set of
sufficient conditions which guarantees the uniqueness of the steady-state
solution and its attractivity. Starting from simple assumptions, we derive
simple criteria that can be efficiently exploited to characterise the behavior
of dissipative systems of spins and bosons (with truncated Fock space), and a
wide variety of other open quantum systems recently studied.
