  We consider a stochastic particle system in which a finite number of
particles interact with one another via a common energy tank. Interaction rate
for each particle is proportional to the square root of its kinetic energy, as
is consistent with analogous mechanical models. Our main result is that the
rate of convergence to equilibrium for such a system is $\sim t^{-2}$, more
precisely it is faster than a constant times $t^{-2+\varepsilon}$ for any
$\varepsilon>0$. A discussion of exponential vs polynomial convergence for
similar particle systems is included.
