Related Experiment Video
Updated: Jul 11, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Analytical solution to transport in Brownian ratchets via the gambler's ruin model
X Z Cheng1, M B A Jalil, Hwee Kuan Lee
1Department of Electrical and Computer Engineering, National University of Singapore, Singapore.
Abstract:
We present an analogy between the classic gambler's ruin problem and the thermally activated dynamics in periodic Brownian ratchets. By considering each periodic unit of the ratchet as a site chain, we calculated the transition probabilities and mean first passage time for transitions between energy minima of adjacent units. We consider the specific case of Brownian ratchets driven by Markov dichotomous noise. The explicit solution for the current is derived for any arbitrary temperature, and is verified numerically by Langevin simulations. The conditions for current reversal in the ratchet are obtained and discussed.
Related Concept Videos
Ideal Solutions
Reynolds Transport Theorem
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Reaction Mechanisms: Rate-limiting Step Approximation
The Entropy as a State Function
Stability of Equilibrium Configuration: Problem Solving
Problem-solving in the context of the stability of equilibrium configuration...
