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Within the Landau-Ginzburg picture of phase transitions, scalar fieldtheories develop phase separation because of a spontaneous symmetry-breakingmechanism. This picture works in thermodynamics but also in the dynamics ofphase separation. Here we show that scalar non-equilibrium field theoriesundergo phase separation just because of non-equilibrium fluctuations driven bya persistent noise. The mechanism is similar to what happens inMotility-Induced Phase Separation where persistent motion introduces aneffective attractive force. We observe that Noise-Induced Phase Separationoccurs in a region of the phase diagram where disordered field configurationswould otherwise be stable at equilibrium. Measuring the local entropyproduction rate to quantify the time-reversal symmetry breaking, we find thatsuch breaking is concentrated on the boundary between the two phases.

Noise-Induced Phase Separation and Time Reversal Symmetry Breaking in active field theories driven by persistent noise