Brownian motor 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 strongly dependent on random thermal noise, Brownian motors are feasible only
Brownian bridge Brownian bridge A Brownian bridge is a continuous-time stochastic process "B"("t") whose probability distribution is the conditional probability distribution of a Wiener process "W"("t") (a mathematical model of Brownian motion) subject to the condition (when standardized) that "W"(T) = 0, so that the process is pinned at the origin at both "t=0" and "t=T". More precisely: The expected value of the bridge is zero, with variance formula_2, implying that the most uncertainty is in the middle of the bridge, with zero uncertainty at the nodes. The covariance of "B"("s") and "B"("t") is "s"(T − "t")/T if "s" < "t". The