A Stochastic, Isokinetic Method for Gibbs Sampling

We first demonstrate the idea of [220] by considering the following SDE with a single degree of freedom  

111 and fi2 are coupling coefficients, and A is a Lagrange multiplier which is chosen to maintain the isokinetic relation involving p and  

Upon reintroduction of this expression in (8.40 -(8.43) this allows us to write a closed-form SDE system for, 2- 

We follow an analogous procedure to that used to study the distribution in the case of the standard isokinetic system, for the moment ignoring the stochastic terms. This requires us to solve the equation 

Integrating over the isokinetic surfacep + p = /6 , and with respect to the variable 2, yields the Gibbs configurational density. 

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