  Within the Landau-Ginzburg picture of phase transitions, scalar field
theories develop phase separation because of a spontaneous symmetry-breaking
mechanism. This picture works in thermodynamics but also in the dynamics of
phase separation. Here we show that scalar non-equilibrium field theories
undergo phase separation just because of non-equilibrium fluctuations driven by
a persistent noise. The mechanism is similar to what happens in
Motility-Induced Phase Separation where persistent motion introduces an
effective attractive force. We observe that Noise-Induced Phase Separation
occurs in a region of the phase diagram where disordered field configurations
would otherwise be stable at equilibrium. Measuring the local entropy
production rate to quantify the time-reversal symmetry breaking, we find that
such breaking is concentrated on the boundary between the two phases.
