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Particles with internal states in force fields show effective advection-diffusion. New methods using large deviation techniques and multiple-scale analysis reveal insights into effective diffusion components for determining kinetic rates.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Theoretical Physics

Background:

  • Particles with unobserved internal states diffusing in force fields exhibit complex behaviors.
  • Effective advection-diffusion describes the macroscopic particle motion, influenced by internal states and external forces.

Purpose of the Study:

  • To introduce and compare two novel methods for analyzing effective advection-diffusion.
  • To investigate systems with both discrete and continuous internal states.
  • To establish a link between theoretical frameworks and experimental measurements.

Main Methods:

  • Large deviation techniques applied to generating functions/functionals.
  • Multiple-scale analysis, including discrete and continuous internal states.
  • Comparison of auxiliary equations derived from both methods and second-order perturbation theory.

Main Results:

  • Effective diffusion comprises an equilibrium term satisfying an Einstein relation and a force-dependent term.
  • Demonstration that multiple-scale analysis auxiliary equations can be derived via large deviation theory.
  • Identification of a method to determine kinetic rates using moments of particle displacement.

Conclusions:

  • The study provides two complementary methods for understanding effective advection-diffusion in systems with internal states.
  • The findings offer a pathway to experimentally determine kinetic rates from measurable quantities.
  • This work bridges theoretical advancements with potential experimental applications in statistical physics.