  We examine how systems in non-equilibrium steady states close to a continuous
phase transition can still be described by a Landau potential if one forgoes
the assumption of analyticity. In a system simultaneously coupled to several
baths at different temperatures, the non-analytic potential arises from the
different density of states of the baths. In periodically driven-dissipative
systems, the role of multiple baths is played by a single bath transferring
energy at different harmonics of the driving frequency. The mean-field critical
exponents become dependent on the low-energy features of the two most singular
baths. We propose an extension beyond mean field.
