Boltzmann Distribution in Molecular Dynamics Simulation?
Within statistical mechanics (SM) a molecular property $X$ is computed by $$\left&lt;{X}\right&gt;_{SM}=\sum^{states}_i X_i p_i$$where $X_i$ is the value of $X$ for energy state $i$ and $p_i$ is the probability of being in energy state $i$ with energy $E_i$:$$p_i=\frac{e^{-E_i/kT}}{\sum_i e^{-E_i/kT}}$$Within molecular dynamics (MD) the corresponding property is computed by$$\left&lt;{X}\right&gt;_{MD}=\frac{1}{M}\sum^M_i X(t_i)$$where $M$ is the number of time-steps and $X(t_i)$ is the value of $X$ at time $t_i$.

You can also compute $\left&lt;{X_{SM}}\right&gt;$ from an MD by finding all the "unique" states (e.g. conformations) and computing their energy.  "Unique" means that even if a state is observed more than once in the MD you only include it once in the sum over states. 

In principle $$\left&lt;X\right&gt;_{SM} = \lim_{t \to \infty} \left&lt;{X}\right&gt;_{MD}$$ but this assumes that the method used to calculate the energy and forces are identical in both calculations.

For example, for MD explicit solvent calculations with periodic boundary conditions it not really possible to calculate the energy of a state ($E_i$).  Also, vibrational effects must be included in $E_i$, which is typically done using the harmonic oscillator approximation, while the MD will include anharmonic effects. Similarly, the harmonic oscillator approximation is quantized (QM) while the vibrations in the MD simulation are not (classical).