We use numerical simulations to compute the equation of state of a suspension of spherical, self-propelled nanoparticles. We study in detail the effect of excluded volume interactions and confinement as a function of the system temperature, concentration and strength of the propulsion. We find a striking non-monotonic dependence of the pressure with the temperature, and provide simple scaling arguments to predict and explain the occurrence of such an anomalous behavior. We conclude the paper by explicitly showing how our results have an important implications for the effective forces exerted by fluids of self-propelled particles on passive, larger components.
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