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Active particles driven by colored noise can be approximately mapped onto asystem that obeys detailed balance. The effective interactions which can bederived for such a system allow to describe the structure and phase behavior ofthe active fluid by means of an effective free energy. In this paper we explainwhy the related thermodynamic results for pressure and interfacial tension donot represent the results one would measure mechanically. We derive a dynamicaldensity functional theory, which in the steady state simultaneously validatesthe use of effective interactions and provides access to mechanical quantities.Our calculations suggest that in the colored-noise model the mechanicalpressure in coexisting phases might be unequal and the interfacial tension canbecome negative.

journal of statistical mechanics

Effective equilibrium states in the colored-noise model for active  matter II. A unified framework for phase equilibria, structure and mechanical  properties