content_image/329279.jpg content_image/329280.jpg content_image/329281.jpg content_image/329282.jpg content_image/329283.jpg content_image/329278.jpg content_image/329277.jpg content_image/329276.jpg content_image/329275.jpg content_image/329273.jpg
where 

<img src='content_image/329279.jpg'>

<img src='content_image/329280.jpg'>

<img src='content_image/329281.jpg'>

<img src='content_image/329282.jpg'>

<img src='content_image/329283.jpg'>

Both in L BKNHC A and L BKNHC B there appears an operator with the form 

<img src='content_image/329278.jpg'>

where ( k, i ) = ( χ, ξ ) for L$_{A}$ and ( k, i ) = ( η, ζ ) for L$_{B}$ . Again following the derivation in Appendix A, we find 

<img src='content_image/329277.jpg'>

The function ( τ p$_{k}$ 2 m$_{k}$ ) − $^{1}$sinh [ τ p$_{k}$ 2 m$_{k}$ ] is treated through an eighth order expansion [37]. 

The propagators 

<img src='content_image/329276.jpg'>

with α = A, B, C can now be introduced. One possible reversible measure-preserving inte- gration algorithm for the BKNHC chain thermostat is then 

<img src='content_image/329275.jpg'>

In pseudo-code form, we have the resulting integration algorithm: 

<img src='content_image/329273.jpg'>

