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We consider the pressure in the steady-state regime of three stochasticmodels characterized by self-propulsion and persistent motion and widelyemployed to describe the behavior of active particles, namely the ActiveBrownian particle (ABP) model, the Gaussian colored noise (GCN) model and theunified colored noise model (UCNA). Whereas in the limit of short but finitepersistence time the pressure in the UCNA model can be obtained by differentmethods which have an analog in equilibrium systems, in the remaining twomodels only the virial route is, in general, possible.  According to this method, notwithstanding each model obeys its own specificmicroscopic law of evolution, the pressure displays a certain universalbehavior. For generic interparticle and confining potentials, we derive aformula which establishes a correspondence between the GCN and the UCNApressures. In order to provide explicit formulas and examples, we specializethe discussion to the case of an assembly of elastic dumbbells confined to aparabolic well. By employing the UCNA we find that, for this model, thepressure determined by the thermodynamic method coincides with the pressuresobtained by the virial and mechanical methods. The three methods when appliedto the GCN give a pressure identical to that obtained via the UCNA. Finally, wefind that the ABP virial pressure exactly agrees with the UCNA and GCN result.

Pressure in an exactly solvable model of active fluid