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Nonequilibrium version of the Einstein relation.

Daniel Hurowitz1, Doron Cohen1

  • 1Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.

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|October 15, 2014
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Summary
This summary is machine-generated.

The Einstein relation for diffusion is broken under nonequilibrium conditions. This study shows the ratio of drift velocity to diffusion coefficient (v/D) depends nonlinearly on system affinity in Brownian motion on a lattice.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Physical Chemistry

Background:

  • The Einstein relation connects diffusion coefficient (D) and drift velocity (v) in equilibrium systems.
  • Nonequilibrium conditions often lead to deviations from classical relations.
  • Brownian motion on a lattice provides a fundamental model for studying transport phenomena.

Purpose of the Study:

  • To investigate the violation of the Einstein relation in nonequilibrium systems.
  • To analyze the emergence of this violation in a simplified Brownian motion model.
  • To understand the dependence of the v/D ratio on system parameters.

Main Methods:

  • Analysis of Brownian motion on a lattice.
  • Consideration of lattice periodicity, randomness, and asymmetric transition rates.
  • Application of the nonequilibrium fluctuation theorem.

Main Results:

  • The Einstein relation is violated under nonequilibrium circumstances.
  • The ratio of drift velocity to diffusion coefficient (v/D) is a nonlinear function of affinity.
  • The v/D ratio exhibits a nontrivial dependence on the microscopic properties of the sample.

Conclusions:

  • The celebrated Einstein relation is not universally valid and breaks down in nonequilibrium systems.
  • The deviation from the Einstein relation is governed by the system's affinity and microscopic details.
  • This finding has implications for understanding transport phenomena in various physical and chemical systems.