Coupled Brownian motors

Abstract

Abstract. A unifying view on several astonishing effects induced by state dependent, uncorrelated fluctuations (multipficative white noise) is presented. The main emphasis of our introductory discussion is put on the basic physical mechanisms at work in a white noise driven "pulsating ratchet", noise-induced non-equilibrium phase transitions, and their synthesis in the form of coupled Brownian motors.

A Review of Parrondo's Paradox

“…Y n can now also be used for game A by letting p 1 = p 2 = p. Having the games represented by non-infinite DTMCs allows useful calculations to be performed, as shown in subsequent sections. For example, from Onsager's Nobel prize winning work on reversible chemical reactions, we can use a detailed balance to quickly determine which direction has the greatest drift: clockwise or counter-clockwise [13,38,39]. The detailed balance simply entails finding the product of probabilities in one direction, and comparing this to the product of the probabilities in the opposite direction.…”

“…Van den Broeck et al [39] use the games to give an example of a discrete "pulsating ratchet." They describe playing the games against Maxwell's demon to highlight their apparent paradoxical nature.…”

New Paradoxical Games Based on Brownian Ratchets

“…It has recently been shown, in the seminal papers [4][5][6][7], that a discrete-time version of the flashing ratchet can be interpreted as simple gambling games. Here we have two losing games which become winning when combined.…”

“…The games originally described in [4][5][6][7] are expressed in terms of tossing biased coins. The games rely on a statedependent rule based on the player's capital and two losing games can surprisingly combine to win.…”

“…Seigman [18,19] has reinterpreted the capital of the games in terms of electron occupancies in energy levels, recasting the problem in terms of rate equations. Similarly, Van den Broeck et al [7] have likened the analysis of the transition probabilities of the games to Onsager's treatment of reaction rates in circular chemical reactions [20]. It has been suggested in [6] that an area of interest to quantum information theory would be to recast the games in terms of quantum probability amplitudes along the lines of [21][22][23].…”