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An alternative equilibrium stochastic dynamics for a Brownian particle ininhomogeneous space is derived. Such a dynamics can model the motion of acomplex molecule in its conformation space when in equilibrium with a uniformheat bath. The derivation is done by a simple generalization of the formulationdue to Zwanzig for a Brownian particle in homogeneous heat bath. We show thatif the system couples to different number of bath degrees of freedom atdifferent conformations then the alternative model is derived. We discussresults of an experiment by Faucheux and Libchaber which probably has indicatedpossible limitation of the Boltzmann distribution as equilibrium distributionof a Brownian particle in inhomogeneous space and propose experimentalverification of the present theory using similar methods.

Equilibrium stochastic dynamics of a Brownian particle in inhomogeneous space: derivation of an alternative model