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Parrondo-like behavior in continuous-time random walks with memory.

Miquel Montero1

  • 1Departament de Física Fonamental, Universitat de Barcelona (UB), Barcelona, Spain. miquel.montero@ub.edu

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Combining two continuous-time random walks (CTRWs), one with memory, can create directed motion. This phenomenon, akin to stochastic resonance, originates from the Parrondo paradox.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Continuous-time random walks (CTRWs) are fundamental models for stochastic processes.
  • Standard CTRWs typically describe unbiased motion.
  • Incorporating memory into stochastic processes presents theoretical challenges.

Purpose of the Study:

  • To demonstrate how combining two unbiased CTRWs can yield a directed process.
  • To explore the role of memory in generating drift.
  • To connect this phenomenon to stochastic resonance and the Parrondo paradox.

Main Methods:

  • Utilizing the continuous-time random walk (CTRW) formalism.
  • Analyzing the random combination of two distinct CTRWs.
  • Investigating the emergent drift in a system where one CTRW possesses memory.

Main Results:

  • A combination of two unbiased CTRWs, with one exhibiting memory, results in a process with significant drift.
  • This drift can be interpreted as a form of stochastic resonance when the unbiased CTRW is viewed as noise.
  • The underlying mechanism is analogous to the Parrondo paradox.

Conclusions:

  • Memory is a key factor in generating directed motion from unbiased stochastic processes.
  • The study provides a novel perspective on stochastic resonance through the lens of CTRWs.
  • The findings highlight a connection between memory effects in random walks and game theory paradoxes.