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conjugate momenta p1 (t)...pn (t), each a function of time, would have to be specified and n the number of atoms. The number of degrees of freedom, n, is, for an assembly of atoms, equal to 3N, for systems composed of molecules, internal degrees of freedom (rotations and vibrations) have to be included as well. Thus, even the simplest thermodynamic system corresponds to a mechanical system of immense complexity. Presenting a diatomic molecule in gas phase, we need a trajectory of momenta values (p1, p2) and a trajectory with positions (q1, q2). For recording the p and q we need to record three coordinates in space x, y and z, like Figure 3-1. q p1 q2 p q1 p2 Figure 3-1: A diatomic molecule in phase space. The position and motion of the particle are presented by a point with coordinates (q1x, q1y, q1z, q2x, q2y, q2z, p1x, p1y, p1z, p2x, p2y, p2z) in a 2- dimensional phase space. A quasi-geometric representation of the dynamical state of a mechanical system, known as phase space specified by the vector x=q, p, has proved to be invaluable in classical statistical mechanics. The phase space for a system having n degrees of freedom is the composite of the n-dimensional configuration space and the n-dimensional momentum space. A point in its 2n-dimensional phase space represents the instanteous state of the system. The representative point traces out a trajectory in the hypothetical space as the system changes with time in accordance with the laws of mechanics. Given the point in phase space representing the state of the system at time t, the future (as well as the past) trajectory is, in principle, completely and uniquely determined. Only in the case n=1, a system having but one degree of freedom, can the 31PDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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