Deterministic Methods

The kind of systems we are dealing with in this chapter are such that all degrees of freedom are explicitly taken into account. We do not allow stochastic elements representing, for example, an interaction of the system with a heat bath. The starting point is a Newtonian, Lagrangian or Hamiltonian formulation within the framework of classical mechanics. What we are interested in is to compute quantities for such systems, for example, thermodynamic variables, which appear as ensemble averages. Due to energy conservation the natural ensemble is the microcanonical one. However, sometimes it is desirable to compute a quantity in a different ensemble. To allow such calculations within the framework of a Newtonian, Lagrangian or Hamiltonian description, the formulation has to be modified. In any case, the formulation leads to differential equations of motion. These equations will be discretized to generate a path in phase space, along which the properties are computed.