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Fluctuation-dissipation relations far from equilibrium: a case study.

Gerhard Jung1, Friederike Schmid2

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This study investigates fluctuation-dissipation theorems (FDTs) in non-equilibrium physics using microrheology simulations. The first FDT breaks down far from equilibrium, while the second FDT remains valid, offering insights into generalized Langevin equations.

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Area of Science:

  • Statistical Physics
  • Soft Matter Physics
  • Non-equilibrium Thermodynamics

Background:

  • Fluctuation-dissipation theorems (FDTs) are crucial in statistical physics, rigorously derived for equilibrium systems.
  • Their extension to non-equilibrium systems remains a significant theoretical challenge and subject of debate.

Purpose of the Study:

  • To investigate the validity of two distinct FDTs in a simulated active microrheology experiment.
  • To determine how system conditions, specifically proximity to or distance from equilibrium, affect FDT applicability.
  • To explore the relationship between memory friction kernels and stochastic forces within generalized Langevin equations (GLEs).

Main Methods:

  • Simulation of an active microrheology experiment involving a colloid pulled through a fluid.
  • Characterization of structural and dynamical properties of near- and far-from-equilibrium systems.
  • Reconstruction of an effective generalized Langevin equation (GLE) to model colloid dynamics.

Main Results:

  • The first FDT, relating non-equilibrium response to equilibrium correlations, was found to be valid near equilibrium but broke down under strong external driving (far from equilibrium).
  • The second FDT, connecting the memory friction kernel to the stochastic force, was consistently fulfilled across all simulated conditions.
  • A mathematical framework was established demonstrating the general validity of the second FDT for memory kernels derived from Volterra equations, even in non-stationary non-equilibrium systems.

Conclusions:

  • The applicability of FDTs in non-equilibrium systems is condition-dependent, with the first FDT showing limited validity.
  • The second FDT provides a robust framework for analyzing non-equilibrium dynamics, particularly within the context of GLEs.
  • Imposing an orthogonality constraint on the stochastic force ensures the second FDT's validity and leads to unique, desirable GLEs for coarse-grained modeling.