content_image/328723.jpg content_image/328724.jpg content_image/328725.jpg
## V. BULGAC-KUSNEZOV-NOS ´ E-HOOVER CHAIN 

For simplicity, we explicitly treat only the case in which the p$_{ζ}$ and p$_{ξ}$ demons are each coupled to a standard NH thermostat (length one). It would be straightforward to couple each of the demons to NH chains [32], and the general case can be easily inferred from what follows. Define the Hamiltonian 

<img src='content_image/328723.jpg'>

Upon defining the phase space point x = ( q, ζ, ξ, η, χ, p, p$_{ζ}$, p$_{ξ}$, p$_{η}$, p$_{χ}$ ) = ( x$_{1}$, x$_{2}$, x$_{3}$, x$_{4}$, x$_{5}$, x$_{6}$, x$_{7}$, x$_{8}$, x$_{9}$, x$_{10}$ ) and the antisymmetric BKNHC tensor 

<img src='content_image/328724.jpg'>

associated non-Hamiltonian equations of motion are 

with i = 1 , . . . , 10. 

<img src='content_image/328725.jpg'>

