  This paper explores the phenomenon of energy relaxation for stars in a galaxy
embedded in a high density environment that is subjected continually to
perturbations reflecting the presence of other nearby galaxies and/or
incoherent internal pulsations. The analysis is similar to earlier analyses of
energy relaxation induced by binary encounters between nearby stars and between
stars and giant molecular clouds in that the perturbations are idealised as a
sum of near-random events which can be modeled as diffusion and dynamical
friction. However, the analysis differs in one important respect: because the
time scale associated with these perturbations need not be short compared with
the characteristic dynamical time t_D for stars in the original galaxy, the
diffusion process cannot be modeled as resulting from a sequence of
instantaneous kicks, i.e., white noise. Instead, the diffusion is modeled as
resulting from random kicks of finite duration, i.e., coloured noise
characterised by a nonzero autocorrelation time t_c. A detailed analysis of
coloured noise generated by sampling an Ornstein-Uhlenbeck process leads to a
simpling scaling in terms of t_c and an effective diffusion constant D.
Interpreting D and t_c following early work by Chandrasekhar (1941) (the
`nearest neighbour approximation') implies that, for realistic choices of
parameter values, energy relaxation associated with an external environment
and/or internal pulsations could be important on times short compared with the
age of the Universe.
