Brownian motor ramifications of the Fluctuation Theorems, Pumping Quantization Theorems, and Pumping-Restriction Theorems. Brownian motor Brownian motors are nano-scale or molecular devices by which thermally activated processes (chemical reactions) are controlled and used to generate directed motion in space and to do mechanical or electrical work. These tiny engines operate in an environment where viscosity dominates inertia, and where thermal noise makes moving in a specific direction as difficult as walking in a hurricane: the forces impelling these motors in the desired direction are minuscule in comparison with the random forces exerted by the environment. Because this type of motor is so
Schramm–Loewner evolution evolution is a probability measure on planar curves, given as the image of Wiener measure under this map. In general the curve γ need not be simple, and the domain "D" is not the complement of γ([0,"t"]) in "D", but is instead the unbounded component of the complement. There are two versions of SLE, using two families of curves, each depending on a non-negative real parameter κ: SLE depends on a choice of Brownian motion on the boundary of the domain, and there are several variations depending on what sort of Brownian motion is used: for example it might start