We study the relation between the partition function of a non--relativistic
particle, in one spatial dimension, 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 using Monte Carlo simulations for computing
the correlation functions that satisfy the corresponding identities. We show
that both can be related to the partition function of the corresponding,
maximally supersymmetric, theory with one--dimensional bosonic worldvolume, by
appropriate analytic continuation, from Euclidian to real time, 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.
Therefore supersymmetry is relevant at the scale in which equilibrium with
the bath is meaningful. At scales when the "true" degrees of freedom of the
bath can be resolved (e.g. atoms and molecules for the case of thermal
fluctuations) the superpartners become "hidden". They can be, always, revealed
through the identities satisfied by the correlation functions of the
appropriate noise field, however.
In fact, the same formalism applies whatever the "microscopic" origin of the
fluctuations.
Therefore, all consistently closed physical systems are supersymmetric--and
any system that is explicitly not invariant under supersymmetric
transformations, is, in fact, open and, therefore, incomplete.Comment: 48 pages, many PNG figures, LaTeX2e. Requires utphys.bst for the
bibliography. v2: Extensively rewritten; errors corrected regarding the
"fermionic'' action and presentation clarified and sharpene