Stochastic Processes in Physics, Chemistry, and Biology

1. Front Matter

   Pages I-X

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2. Stochastic Transport and Brownian Motion

   1. Directed Current Without Dissipation: Reincarnation of a Maxwell—Loschmidt Demon

      • Igor Goychuk, Peter Hänggi

      Pages 7-20

   2. Molecular Motors and Stochastic Models

      • Reinhard Lipowsky

      Pages 21-31

   3. Nonlinearly Coupled Chemical Reactions

      • Martin Bier, Marcin Kostur

      Pages 32-37

   4. Thermodynamics of Isothermal Brownian Motors

      • Juan M.R. Parrondo, Borja Jiménez de Cisneros, Ricardo Brito

      Pages 38-49

   5. Rocking Ratchets at High Frequencies

      • Peter Reimann

      Pages 50-60

   6. Defect Dragging in Periodic Structures

      • M. Borromeo, F. Marchesoni

      Pages 61-68

   7. Conduction in an Inhomogeneous Medium

      • Nico G. van Kampen

      Pages 69-74

   8. Theory and Control of Multiple Hopping in Activated Surface Diffusion

      • Eli Pollak

      Pages 75-84

   9. Brownian Motion in a d-Dimensional Space with Fluctuating Friction

      • Peter Talkner, Jerzy Łuczka

      Pages 85-96

   10. Active Motion of Brownian Particles

       • Frank Schweitzer

       Pages 97-106

   11. Diffusion in Granular Gases of Viscoelastic Particles

       • Nikolai V. Brilliantov, Thorsten Pöschel

       Pages 107-117

3. Stochastic Resonance and Phase Synchronization

   1. Scaling of Noise and Constructive Aspects of Fluctuations

      • J. M. G. Vilar, J. M. Rubí

      Pages 121-130

   2. Stochastic Resonances in Underdamped Bistable Systems

      • Luca Gammaitoni, Adi R. Bulsara

      Pages 131-138

   3. Stochastic Resonance in a System of Coupled Asymmetric Resonators

      • Robert Rozenfeld, Benjamin Lindner

      Pages 139-149

   4. Optimizing Information Transmission in Model Neuronal Ensembles: The Role of Internal Noise

      • Nigel G. Stocks

      Pages 150-159

   5. Stochastic Resonance with Images and Spatially Correlated Stochastic Patterns

      • Jan A. Preund

      Pages 160-171

   6. Adiabatic and Non-adiabatic Resonances in Excitable Systems

      • André Longtin

      Pages 172-181

   7. The Lighthouse Model of a Neural Net with Delay

      • Hermann Haken

      Pages 182-189

   8. Noise-enhanced Phase Coherence in Ensembles of Stochastic Resonators

      • Alexander Neiman

      Pages 190-201

The theory of stochastic processes originally grew out of efforts to describe Brownian motion quantitatively. Today it provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. The credit for acquiring all the deep insights and powerful methods is due ma- ly to a handful of physicists and mathematicians: Einstein, Smoluchowski, Langevin, Wiener, Stratonovich, etc. Hence it is no surprise that until - cently the bulk of basic and applied stochastic research was devoted to purely mathematical and physical questions. However, in the last decade we have witnessed an enormous growth of results achieved in other sciences - especially chemistry and biology - based on applying methods of stochastic processes. One reason for this stochastics boom may be that the realization that noise plays a constructive rather than the expected deteriorating role has spread to communities beyond physics. Besides their aesthetic appeal these noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for so far open pr- lems (information transmission in the nervous system and information p- cessing in the brain, processes at the cell level, enzymatic reactions, etc.). They may also pave the way to novel technological applications (noise-- hanced reaction rates, noise-induced transport and separation on the na- scale, etc.). Key words to be mentioned in this context are stochastic r- onance, Brownian motors or ratchets, and noise-supported phenomena in excitable systems.

• Brownian motion
• Potential
• Stochastic processes
• information processing
• stochastic process
• thermodynamics

• Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany

  Jan A. Freund

• Charité, Institut für Biochemie, Humboldt-Universität zu Berlin, Berlin, Germany

  Thorsten Pöschel

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