Quantum mechanical explanation for Le Chatelier's principle?
The main thing that classical and quantum statistical mechanics have in common is probability.  In classical stat mech the equilibrium value of an observable is given by
$$\langle A \rangle = \sum_i^N p_iA_i$$
where $A_i$ is the value of $A$ in microstate $i$ and $p_i$ is the probability of microstate $i$.  The expression for $p_i$ at equilibrium depends on the ensemble (microcanonical, canonical, etc).  One way to define equilibrium is that the probabilities are constant
$$\frac{\partial p_i(t)}{\partial t}=0$$
So if one perturbs the system so that this equation doesn't hold the $p_i$'s will change until it does and Le Chatelier's principle is a heuristic way of predicting whether the individual $p_i$'s increase or decrease.

In quantum stat mech the equilibrium value of an observable is given by
$$ \langle A \rangle = \tfrac{1}{N} \sum_\alpha^N \langle \Psi^{\alpha}| \hat{A} |\Psi^{\alpha}\rangle$$
where $\Psi^{\alpha}$ is the wavefunction for microstate $\alpha$

The wavefunctions are typically expanded in an orthonormal basis ($\phi$'s)
$$ \langle A \rangle = \tfrac{1}{N} \sum_{k,l} \rho_{l,k}\langle \phi_l| \hat{A} |\phi_k\rangle $$
where the density matrix is can be defined by a density operator
$$ \rho_{l,k} = \langle \phi_k| \hat{\rho} |\phi_l\rangle $$

The equilibrium is then defined as 
$$\frac{\partial \hat{\rho}(t)}{\partial t}=0$$

So if one perturbs the system so that this equation doesn't hold the $\hat{\rho}$ will change until it does and Le Chatelier's principle is a heuristic way of predicting whether the individual $\Psi^{\alpha}$ contributions to  $\hat{\rho}$ increase of decrease.

The time dependence of $\hat{\rho}$ can be calculated by the time-dependent Schrödinger equation.  So Le Chatelier's principle is a heuristic way of predicting roughly how the time-dependent wavefunctions will evolve at the simulation approaches equilibrium.  

To get a more physical picture one can introduce the Born-Oppenheimer approximation in which case the numerical simulation of the time-dependent Schrödinger equation becomes a classical MD simulation (with a QM energy function) from which the time dependence of the probabilities $p_i$ can be computed and Le Chatelier's principle is a heuristic way of predicting whether the individual $p_i$'s increase or decrease.