## 7.1.2 Nosé-Hoover dynamics

Instead of perfectly constraining the kinetic energy, one may introduce a sort of thermostat which acts to keep the energy near a desired value. Nosé has shown that under quite general conditions the spread around the given is such that a canonical distribution is approached.

Hoover rewrote Nosé's original equations of motion in the following simple way:
 (7.7) (7.8) (7.9)

where we have omitted the particle index . The coupling parameter represents the efficiency of the thermal bath holding the temperature constant. is a kind of viscosity'' which, however, may take on negative values.

Nosé has shown that the phase space trajectory of such a system will under very general assumptions (a few interacting particles suffice) lead to canonical averaging. (See also Posch, Hoover, Vesely Phys.Rev.A 33(1986)4253.)

For the spread of around approaches zero, and the Nosé-Hoover dynamics becomes identical to Gauss dynamics.
F. J. Vesely / University of Vienna