  Combined-resolution simulations are an effective way to study molecular
properties across a range of length- and time-scales. These simulations can
benefit from adaptive boundaries that allow the high-resolution region to adapt
(change size and/or shape) as the simulation progresses. The number of degrees
of freedom required to accurately represent even a simple molecular process can
vary by several orders of magnitude throughout the course of a simulation, and
adaptive boundaries react to these changes to include an appropriate but not
excessive amount of detail. Here, we derive the Hamiltonian and distribution
function for such a molecular simulation. We also design an algorithm that can
efficiently sample the boundary as a new coordinate of the system. We apply
this framework to a mixed explicit/continuum representation of a peptide in
solvent. We use this example to discuss the conditions necessary for a
successful implementation of adaptive boundaries that is both efficient and
accurate in reproducing molecular properties.
