Equilibrium of a mesoscopic system with conformation dependent damping: An alternative approach

We look at the dynamics of a Brownian particle with internal degrees of freedom and conformation dependent damping. Inhomogeneous damping apparently makes the problem a stochastic process with multiplicative noise. We derive the equilibrium distribution of such a system on the basis of a single postulate that the stochastic forces on the system produces no drift. Based on this postulate, we generalize the expression of the stochastic force for the equilibrium of such systems. The equilibrium probability distribution obtained deviates from the exact canonical form, although, the equipartition of energy remains intact when the internal degrees of freedom are integrated out. We also show a crucial local balance of the rate of average energy inflow and outflow as a consequence of the equilibrium probability distribution.