  We propose a mean-field theory for nonequilibrium phase transitions to a
periodically oscillating state in spin models. A nonequilibrium generalization
of the Landau free energy is obtained from the join distribution of the
magnetization and its smoothed stochastic time derivative. The order parameter
of the transition is a Hamiltonian, whose nonzero value signals the onset of
oscillations. The Hamiltonian and the nonequilibrium Landau free energy are
determined explicitly from the stochastic spin dynamics. The oscillating phase
is also characterized by a non-trivial overlap distribution reminiscent of a
continuous replica symmetry breaking, in spite of the absence of disorder. An
illustration is given on an explicit kinetic mean-field spin model.
