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
Brownian meander Brownian meander In the mathematical theory of probability, Brownian meander formula_1 is a continuous non-homogeneous Markov process defined as follows: Let formula_2 be a standard one-dimensional Brownian motion, and formula_3, i.e. the last time before "t" = 1 when formula_4 visits formula_5. Then the Brownian meander is defined by the following: In words, let formula_7 be the last time before 1 that a standard Brownian motion visits formula_5. (formula_9 almost surely.) We snip off and discard the trajectory of Brownian motion before formula_7, and scale the remaining part so that it spans a time interval of length 1. The scaling