  A paradigm for isothermal, mechanical rectification of stochastic
fluctuations is introduced in this paper. The central idea is to transform
energy injected by random perturbations into rigid-body rotational kinetic
energy. The prototype considered in this paper is a mechanical system
consisting of a set of rigid bodies in interaction through magnetic fields. The
system is stochastically forced by white noise and dissipative through
mechanical friction. The Gibbs-Boltzmann distribution at a specific temperature
defines the unique invariant measure under the flow of this stochastic process
and allows us to define ``the temperature'' of the system. This measure is also
ergodic and weakly mixing. Although the system does not exhibit global directed
motion, it is shown that global ballistic motion is possible (the mean-squared
displacement grows like t squared). More precisely, although work cannot be
extracted from thermal energy by the second law of thermodynamics, it is shown
that ballistic transport from thermal energy is possible. In particular, the
dynamics is characterized by a meta-stable state in which the system exhibits
directed motion over random time scales. This phenomenon is caused by
interaction of three attributes of the system: a non flat (yet bounded)
potential energy landscape, a rigid body effect (coupling translational
momentum and angular momentum through friction) and the degeneracy of the
noise/friction tensor on the momentums (the fact that noise is not applied to
all degrees of freedom).
