Mr. Zhaoyang,

The free Gibbs energy term.

Molecular dynamics relies on relatively simple forcefields to describe the interparticle forces, and also uses classical mechanics to represent and integrate the equations of motion. So, in principle, it will reproduce the classical results that you can get from lattice dynamics such as elasticity and propagation of different modes of waves. But the quantum mechanical behavior such as Einstein and Debye heat capacities at low temperature or quantization in phonon dispersion will be missing from the classical MD simulations.

Lattice dynamics (LD) is used to study the vibrational properties of materials, generally in equilibrium (although there are techniques for nonequilibrium LD methods as well). A lattice dynamics model provides the normal modes of vibrations of a system of N coupled particles, the key of which is the definition of the Hessian (or dynamical) matrix from an underlying interatomic potential (which can be classical, semi-empirical, or quantum mechanical). The Hessian is the Laplacian of the interatomic potential energy function. With these methods you can get phonon densities of states, dispersion relations, elastic constants, sound velocities, etc.

Molecular dynamics (MD) uses nominally the exact same interatomic potential, but it uses it to calculate the instantaneous forces existing in the material and integrate the equations of motion in time of the same system of N particles under some statistical ensemble (microcanonical, canonical, etc). In this way you can study all kinds of nonequilibrium phenomena, which is what makes MD so extremely useful.

So I wouldn't say that the difference between LD and MD is in the physical nature of the force field -as Mohsen indicates-, as that is nominally the same in both (it is now common to run 'ab initio' -i.e. quantum- MD simulations), but in the nature of the physical properties that it can simulate/provide.