  We study a gas containing two components, a small component P and a large
component Q. P is selectively heated to a high temperature and then returns to
equilibrium via collisions with Q. This thermal equilibration process is
analysed in a new way. We divide the kinetic energy space of the molecules of P
into two regions F and D, and show that the molecules of P randomly switch
(`oscillate') between the two states as time proceeds due to collisions with
the molecules of Q. Initially, the molecules of P are all in the state D,
however because each molecule in P collides with the molecules of Q at
different times, the oscillations occur out of step with each other. There is a
net destructive interference between the oscillations, and so they are not
observed when monitoring the average kinetic energy of the molecules of P as a
function of time. We will explain the similarities and differences between this
observation and transverse relaxation processes that occur in magnetic
resonance spectroscopy. This study employs a stochastic model of elastic
collisions between the molecules of P and Q, and for completeness we examine
its relationship with the two major models of thermal equilibration in
statistical physics, namely the Boltzmann equation and the Ornstein-Uhlenbeck
process.
