  We study the relation between the partition function of a non--relativistic
particle, that describes the equilibrium fluctuations implicitly, and the
partition function of the same system, deduced from the Langevin equation, that
describes the fluctuations explicitly, of a bath with additive white--noise
properties. We show that both can be related to the partition function of an
${\mathcal N}=1$ supersymmetric theory with one--dimensional bosonic
worldvolume and that they can all describe the same physics, since the
correlation functions of the observables satisfy the same identities for all
systems.The supersymmetric theory provides the consistent closure for
describing the fluctuations, even though supersymmetry may be broken, when
their backreaction is taken into account. The trajectory of the classical
particle becomes a component of a superfield, when fluctuations are taken into
account. These statements can be tested by the identities the correlation
functions satisfy, by using a lattice regularization of an action that
describes commuting fields only.
