Brownian motion apart once the particle is in motion. Also, there would be a distribution of different possible Δ"V"s instead of always just one in a realistic situation. The diffusion equation yields an approximation of the time evolution of the probability density function associated to the position of the particle going under a Brownian movement under the physical definition. The approximation is valid on short timescales. The time evolution of the position of the Brownian particle itself is best described using Langevin equation, an equation which involves a random force field representing the effect of the thermal fluctuations of the solvent on
Brownian motor at the nanometer scale. The term "Brownian motor" was originally coined by Peter Hänggi in 1995: A distinct feature of a Brownian motor is—in contrast to a molecular motor—that the output response is typically coupled only loosely to the input perturbation and action of fluctuations. In biology, many protein-based molecular motors in the cell may in fact be Brownian motors. These molecular motors convert the chemical energy present in ATP into mechanical energy. One example of a Brownian motor would be an ATPase motor that hydrolyzes ATP to generate fluctuating anisotropic energetic potentials. The anisotropic potentials along the path would