2. Calculating a molecular dynamics trajectory

For a system of N atoms, 6N values are needed to define the state of the system (three coordinate values and three velocity values per atom). Each combination of these values gives a point in 6N-dimensional space; this space is called phase space, and a trajectory configuration is therefore a collection of points in this space.

Molecular dynamics trajectory calculations are always performed under the ergodic assumption, i.e. that the average of a quantity over a set of equivalent particles is equal to the time average of a particle. This axiom of statistical mechanics makes it possible to calculate average system properties from a molecular dynamics simulation. If it were possible to visit all points in the phase space, the trajectory would be called ergodic and would not depend on the initial configuration. In practice, phase space is immense, and an ergodic trajectory...