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Entropy Change in Reversible Processes

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Fluctuation effects in the pair-annihilation process with Lévy dynamics.

Ingo Homrighausen1, Anton A Winkler, Erwin Frey

  • 1Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2013
PubMed
Summary
This summary is machine-generated.

Particle pair annihilation exhibits density decay governed by anomalous diffusion via Lévy flights. Critical dimension shifts, breaking the law of mass action due to long-range fluctuations and revealing universal behavior near critical points.

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Area of Science:

  • Statistical Physics
  • Chemical Kinetics
  • Complex Systems

Background:

  • Investigating density decay in pair-annihilation reactions (A+A→∅) on a cubic lattice.
  • Incorporating anomalous diffusion through Lévy flights, characterized by long-range jumps and superdiffusive behavior.

Purpose of the Study:

  • To study the system near the critical dimension where the law of mass action breaks down.
  • To analyze the consequences of long-range fluctuations on reaction rates and universality.

Main Methods:

  • Utilizing nonperturbative renormalization group theory to analyze systems close to the critical dimension.
  • Examining two specific implementations of Lévy flights to understand crossover to normal diffusion.

Main Results:

  • The critical dimension is found to depend continuously on the Lévy flight distribution parameter.
  • Long-range fluctuations cause anticorrelations, violating the well-stirred reactant assumption and breaking the law of mass action.
  • A universal law approximates the renormalized reaction rate near the critical dimension, and nonanalytic power law corrections emerge.

Conclusions:

  • Long-range fluctuations significantly alter reaction dynamics, leading to emergent universality and breakdown of classical kinetics.
  • The study highlights the importance of anomalous diffusion in understanding complex reaction systems near critical points.