all the degrees of freedom of a system. This is, of course, an example of nonuniform limits. We are interested in taking both $\tau_\mathrm{sim}
\rightarrow \infty$ and $\tau_\mathrm{equ} \rightarrow \infty$, where $\tau_\mathrm{sim}$ is the representative simulation time and $\tau_\mathrm{equ}$ is the equipartition time (which is proportional to the “stiffness” of the constraints). In constrained molecular dynamics, we take the limit $\tau_\mathrm{equ} \rightarrow \infty$ first, which prevents equipartition from occurring; whereas in equilibrium statistical mechanics, we take $\tau_\mathrm{sim}
\rightarrow \infty$ first and this allows energy equipartition. If we are attempting to compute an equilibrium quantity, such as the free energy of binding, it is essential to allow energy equipartition. Understanding this distinction explains the apparently contradictory results for constrained and unconstrained averages for a flexible trimer [@frenkel02 §15.1].

One way of understanding the constrained equilibrium system is to consider how the equilibrium distribution varies as the constraint is imposed. In the limit, the distribution collapses to a lower-dimensional sub-manifold of configuration space. However, this sub-manifold has a “thickness” that depends on the details of the constraint term and, consequently, Monte Carlo moves for the constrained system need to reflect this thickness in order to sample the distribution correctly. As a consequence, 