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