Non-Newtonian Dynamics-Based Iterations for Molecular Sampling

Thermostat Convergence rate Error (to lowest order in t) Efficiency 

5 Non-Newtonian Dynamics-Based Iterations for Molecular Sampling 

There is essentially no need to use maps based on Newtonian deterministic dynamics. There are many alternative dynamics models which leave invariant the canonical measure, going well beyond those considered so far. To illustrate this with one intriguing example, we explore here the stochastic dynamical system in 21S + 1 variables defined by 

For this system, it is possible to show that the Hormander condition holds. Setting all parameters to 1 and taking M = I (without loss of generality in this demonstration) we write our SDE in the form d p = D+ T.dWi, where p is the vector of all 

Now consider the splitting into deterministic and OU parts. The deterministic part 

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