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In a previous paper [Gholami et al. Adv.Th.Sim.4, 2000303 (2021)], we haveidentified a precise relation between the chemical potential of a fullyatomistic simulation and the simulation of an open system in the adaptiveresolution method (AdResS). The starting point was the equivalence derived fromthe statistical partition functions between the grand potentials, $\Omega$, ofthe open system and of the equivalent subregion in the fully atomisticsimulation of reference. In this work, instead, we treat the identity for thegrand potential based on the thermodynamic relation $\Omega=-pV$ andinvestigate the behaviour of the pressure in the coupling region of theadaptive resolution method (AdResS). We confirm the physical consistency of themethod for determining the chemical potential described by the previous workand strengthen it further by identifying a clear numerical relation between thepotential that couples the open system to the reservoir on the one hand and thelocal pressure of the reference fully atomistic system on the other hand. Sucha relation is of crucial importance in the perspective of coupling the AdResSmethod for open system to the continuum hydrodynamic regime.

On the relation between pressure and coupling potential in adaptive resolution simulations of open systems in contact with a reservoir