  An alternative equilibrium stochastic dynamics for a Brownian particle in
inhomogeneous space is derived. Such a dynamics can model the motion of a
complex molecule in its conformation space when in equilibrium with a uniform
heat bath. The derivation is done by a simple generalization of the formulation
due to Zwanzig for a Brownian particle in homogeneous heat bath. We show that
if the system couples to different number of bath degrees of freedom at
different conformations then the alternative model is derived. We discuss
results of an experiment by Faucheux and Libchaber which probably has indicated
possible limitation of the Boltzmann distribution as equilibrium distribution
of a Brownian particle in inhomogeneous space and propose experimental
verification of the present theory using similar methods.
