molecular dynamics

Build a virtual box of atoms, give each one a starting position and velocity, work out the force every atom exerts on every other, and then simply let Newton's laws play forward in tiny time steps. Molecular dynamics is exactly that: running the microscopic movie of matter and watching bulk behaviour, like melting, diffusion, or a protein folding, emerge from the choreography of individual particles.

For N particles interacting through a potential energy U(r_1, ..., r_N), the force on atom i is F_i = -gradient of U with respect to r_i, and you integrate Newton's equation m_i d^2 r_i / dt^2 = F_i for every atom simultaneously. The integrator of choice is almost always Verlet or velocity-Verlet, because it conserves energy well over the millions of steps a run demands. A workhorse model interaction is the Lennard-Jones potential, U(r) = 4 epsilon [ (sigma / r)^12 - (sigma / r)^6 ], whose steep positive term captures short-range repulsion and whose negative term captures long-range attraction. Thermodynamic quantities like pressure or temperature are then recovered as time averages along the trajectory, which equal ensemble averages under the ergodic hypothesis.

You meet molecular dynamics in materials science, chemistry, biophysics (protein folding, membranes), and nanoscale fluid flow. The honest caveats are two. First, standard MD is classical Newtonian dynamics driven by an empirical force field, so it cannot break or form chemical bonds or move electrons unless you upgrade to far costlier ab initio (quantum) MD. Second, the time step must be a few femtoseconds to resolve atomic vibrations, while interesting biology unfolds over microseconds to seconds, so the reachable timescale is a perennial bottleneck and rare events may simply never be sampled.