The paradox of Parrondo's games

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 456, Issue 1994, 2000, Pages 247-259

  Harmer, Gregory P ^a   Abbott, Derek ^a   Taylor, Peter G ^a  

^a UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

Brownian ratchet; Discrete time markov chains; Gambling paradox

Indexed keywords

EID: 0042993577     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0516     Document Type: Article

References (17)

1. Abbott, D., Davis, B. R. & Parrondo, J. M. R. 2000 The problem of detailed balance for the Feynman-Smoluchovvski engine (FSE) and the multiple pawl paradox. In Proc. 2nd Int. Conf. on Unsolved Problems of Noise and Fluctuations (ed. D. Abbott & L. B. Kiss). American Institite of Physics. (In the press.)
2. Astumian, R. D. 1997 Thermodynamics and kinetics of a Brownian motor. Science 276, 917-922.
3. Astumian, R. D. & Bier, M. 1994 Fluctuation driven ratchets: molecular motors. Phys. Rev. Lett. 72, 1766-1769.
4. Bier, M. 1997o Brownian ratchets in physics and biology. Contemp. Phys. 38, 371-379.
5. Bier, M. 19976 A motor protein model and how it relates to stochastic resonance, Feynman's ratchet, and Maxwell's demon. In Stochastic dynamics, vol. 386, pp. 81-87.Springer.
6. Doering, C. R. 1995 Randomly rattled ratchets. Nuovo (7im.'D17, 685-697.
7. Faucheux, L. P., Bourdieu, L. S., Kaplan, P. D. & Libchaber, A. J. 1995 Optical thermal ratchet. Phys. Rev. Lett. 74, 1504-1509.
8. Feynman, R. P., Leighton, R. B. & Sands, M. 1963 The Feynman lectures on physics, vol. 1, pp. 46.1-46.9. Reading, MA: Addison-Wesley.
9. Harmer, G. P. & Abbott, D. 1999 Parrondo's paradox. Statistical Science 14, 206-213.
10. Hänggi, P. & Bartussek, R. 1996 Brownian rectifiers: how to convert Brownian motion into directed transport. In Nonlinear physics of complex systems-current status and future trends. Lecture Notes in Physics, vol. 476, pp. 294-308. Springer.
11. Hughes, B. D. 1995 Random walks and random variables, vol. 1. Oxford University Press.
12. Karlin, S. & Taylor, H. M. 1975 A first course in stochastic processes. Academic.
13. Magnasco, M. O. 1993 Forced thermal ratchets. Phys. Rev. Lett. 71, 1477-1481.
14. Parrondo, J. M. R. & Espanol, P. 1996 Criticism of Feynman's analysis of the ratchet as an engine. Am. 31 Phys. 64, 1125-1130.
15. Rousselet, J., Salome, L., Ajdari, A. & Prost, J. 1994 Directional motion of Brownian particles induced by a periodic asymmetric potential. Nature 370, 446-448.
16. Shlesinger, M. F. 1996 A brief history of random processes. In Proc. 1st Int. Conf. on Unsolved Problems of Noise (ed. Ch. R. Doering, L. B. Kiss & M. F. Shlesinger), pp. 3-10. World Scientific.
17. von Smoluchowski, M. 1912 Experimentall nachweisbare, der üblichen Thermodynamic widersprechende Molekularphänomene. Physikalische Zeitschrift, XIII, 1069-1080.