Discrete and continuous ratchets: from coin toss to molecular motor
David Heath - Department of Mathematical Sciences, Carnegie Mellon University, Pittsburg, PA 15213, United States (email)
Directed motion or ratchet-like behavior in many molecular scale
systems is a consequence of diffusion mediated transport. The Brownian motor
serves as a paradigm. The Parrondo Paradox is a pair of coin toss games, each
of which is fair, or even losing, but become winning with a schedule of playing
them in alternation. It has been proposed as a discrete analog of the Brownian
motor. We examine the relationship between these two systems. We discover
a class of Parrondo games with unusual ratchet-like behavior and for which
diffusion plays a fundamentally different role than it does in the Brownian
motor. Detailed balance is an important feature in these considerations.
Keywords: Diffusion mediated transport, Brownian motor, Parrondo Paradox.
Revised: November 2001; Published: February 2002.
2011 Impact Factor.921