Adaptive resolution techniques are powerful methods for the efficient simulation of soft matter systems in which they simultaneously employ atomistic and coarse-grained (CG) force fields. In such simulations, two regions with different resolutions are coupled with each other via a hybrid transition region, and particles change their description on the fly when crossing this boundary. Here we show that the relative entropy, which provides a fundamental basis for many approaches in systematic coarse-graining, is also an effective instrument for the understanding of adaptive resolution simulation methodologies. We demonstrate that the use of coarse-grained potentials which minimize the relative entropy with respect to the atomistic system can help achieve a smoother transition between the different regions within the adaptive setup. Furthermore, we derive a quantitative relation between the width of the hybrid region and the seamlessness of the coupling. Our results do not only shed light on the what and how of adaptive resolution techniques but will also help setting up such simulations in an optimal manner.

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In practice, the way the force fields are interpolated in the force-based model can vary: for example, instead of using the average of the resolution values λ of two molecules, as in Eq. (1), one can use the product.48,54,74 These different schemes behave similar though. Therefore, we use the FB approach here as a representative of the class of force-based schemes in general.

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