  We introduce a class of exactly solvable models which exhibit an ordering
noise-induced phase transition driven by an entropic mechanism. In contrast
with previous studies, order does not appear in this case as a result of an
instability of the disordered phase produced by noise, but of a balance between
the relaxing deterministic dynamics and the randomizing (entropic) character of
the fluctuations. A finite-size scaling analysis of the phase transition
reveals that it belongs to the universality class of the equilibrium Ising
model. All these results are analyzed in the light of the nonequilibrium
probability distribution of the system, which can be derived analytically. The
relevance of our result as a possible scenario of the so-called Lower Critical
Solution Temperature (LCST) transitions is analysed.
