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In this paper we compare the Boltzmann distribution with a modified Boltzmanndistribution, that results from an It\^o-process considering thermalequilibrium of a Brownian particle with coordinate dependent diffusion, in thelight of an existing experiment. The experiment was reported in 1994 byFaucheux and Libchaber. The experiment made use of direct tracking of diffusionof Brownian particles near a wall. Results of this experiment allows us tocompare the Boltzmann and the modified Boltzmann distribution without makinguse of any adjustable parameter. A comparison of these two distributions withthe experimental results lends support to the consideration of thermodynamicequilibrium of a Brownian particle with coordinate-dependent diffusion to be anIt\^o-process.

Thermal equilibrium of a Brownian particle with coordinate dependent  diffusion: comparison of Boltzmann and modified Boltzmann distributions with  experimental results