Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / Section G / 31 / d / i / Solution

With an attractive Lennard-Jones potential and $k_{B}T\ll ϵ$, a short run can remain trapped in an initial conformation or a metastable compact state. A distance trace may show a long apparently stationary segment, an initial collapse, or occasional jumps between local structures; its histogram depends on initialization and is not necessarily an equilibrium distribution. An extended start need not collapse on the available run length, and a compact start need not already be the global minimum.

Accepting only downhill moves would make this trapping worse and would not sample the specified finite-temperature canonical ensemble. The sketch should therefore label this trace as unequilibrated and avoid assigning its mean a thermodynamic interpretation.