Boltzmann distribution over initial conditions

Hi everyone,

I’m interested in modeling a system where the initial conditions are very important. Initially, I need my system to be in thermal equilibrium both in position and in velocity. For example, imagine my particle has a potential energy U=x^2 (cubic).
I’m simulating a lot of independent particles, and I need their velocities to be thermally equilibrated, but ALSO their positions to be thermally equilibrated. That is, not every particle has to be at x=0, but if a particle is at x=0.5, as its potential energy is higher, its initial velocity must be lower.

Due to the nature of my real problem (there are many stable positions on my potential), I need to define this in my initial conditions and cannot let the system equilibrate (or some particles may have gone to another stable position).

Is there any way of doing this in LAMMPS?

Thanks a lot!!!