  We extend the work of Tanase-Nicola and Kurchan on the structure of diffusion
processes and the associated supersymmetry algebra by examining the responses
of a simple statistical system to external disturbances of various kinds. We
consider both the stochastic differential equations (SDEs) for the process and
the associated diffusion equation. The influence of the disturbances can be
understood by augmenting the original SDE with an equation for {\it slave
variables}. The evolution of the slave variables describes the behaviour of
line elements carried along in the stochastic flow. These line elements
together with the associated surface and volume elements constructed from them
provide the basis of the supersymmetry properties of the theory. For ease of
visualisation, and in order to emphasise a helpful electromagnetic analogy, we
work in three dimensions. The results are all generalisable to higher
dimensions and can be specialised to one and two dimensions. The
electromagnetic analogy is a useful starting point for calculating asymptotic
results at low temperature that can be compared with direct numerical
evaluations. We also examine the problems that arise in a direct numerical
simulation of the stochastic equation together with the slave equations. We pay
special attention to the dependence of the slave variable statistics on
temperature. We identify in specific models the critical temperature below
which the slave variable distribution ceases to have a variance and consider
the effect on estimates of susceptibilities.
