Constant Temperature Molecular Dynamics Methods

How the canonical distribution is realized in simulations based on deterministic dynamical equations is explained in this review. Basic formulations and their recent extensions of two constant temperature molecular dynamics methods; the constraint and the extended system methods, are discussed. In both methods, the canonical distribution is derived analytically as a stationary solution of a generalized Liouville's equation which expresses the conservation of probability in a phase space. In the constraint method, the total kinetic energy of a system is kept to a constant by imposing a constraint. The extended system method replaces a macroscopic heat bath by an additional degree of freedom. The addition of only degree of freedom is enough to derive the canonical distribution. Originally, the control of the kinetic energy is aimed, but recent developments reveal that the canonical distribution is attained by controlling only a ratio of any pair of quantities to a ratio of their canonical ensemble averages. The method is now applicable even to a system which does not have a kinetic energy term. A classical spin system is a typical example.