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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Decelerating microdynamics can accelerate macrodynamics in the voter model.

Hans-Ulrich Stark1, Claudio J Tessone, Frank Schweitzer

  • 1Chair of Systems Design, ETH Zurich, CH-8032 Zurich, Switzerland.

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|September 4, 2008
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Summary

Slowing down microscopic dynamics in the voter model can paradoxically speed up system ordering. This memory-dependent transition rate accelerates reaching a macroscopically ordered state, even in complex networks.

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Area of Science:

  • Statistical physics
  • Complex systems

Background:

  • The voter model is a fundamental framework for studying opinion dynamics and social influence.
  • Understanding how macroscopic order emerges from microscopic interactions is crucial in various scientific fields.

Purpose of the Study:

  • To investigate the impact of memory-dependent transition rates on the ordering dynamics of the voter model.
  • To explore how the time a spin spends in its current state affects the system's overall ordering process.

Main Methods:

  • Simulations of the voter model with a modified transition rate.
  • Analysis of ordering dynamics across different network topologies, including fully connected networks.

Main Results:

  • Counterintuitively, decreasing the transition rate with time spent in a state accelerates system ordering.
  • The ordering process is driven by two competing mechanisms: stabilization of the majority or minority state.
  • The acceleration of ordering is observed across various network structures.

Conclusions:

  • Memory-dependent dynamics can enhance the speed of reaching macroscopic order in spin systems.
  • The findings extend beyond the voter model to other spin systems, highlighting a general principle.
  • Slowing down microscopic processes can be a strategy to expedite collective ordering.