  Adaptive resolution molecular dynamics (MD) schemes allow for changing the
number of degrees of freedom on the fly and preserve the free exchange of
particles between regions of different resolution. There are two main
alternatives on how to design the algorithm to switch resolution using
auxiliary ''switching'' functions; force based and potential energy based
approach. In this work we show that, in the framework of classical MD, the
latter presents fundamental conceptual problems which make unlikely, if not
impossible, the derivation of a robust algorithm based on the potential energy.

Statistical Mechanics