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Theoretical and numerical comparison of some sampling methods for
molecular dynamics

#### Frederic Legoll, *
IMA*

Many properties of chemical systems (such as the pressure inside a liquid,
or radial distributions) are defined as phase space averages of functions
depending on the state of the system. A common way to compute these
averages is to use Molecular Dynamics and to compute time averages on long
trajectories.
When considering systems at constant temperature, the problem amounts to
finding a dynamics which is ergodic for the canonical (or Gibbs) measure.
Many different methods have been proposed in this vein, some of them based
on deterministic dynamics (Hamiltonian or not), some of them based on
stochastic differential equations (such as the Langevin equation). We will
review some theoretical properties of the various methods, provide some
new convergence results and compare the numerical efficiency of the
methods on some simple examples.

This work is joint with Eric Cances and Gabriel Stoltz.