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This study derives inhomogeneous two-time correlation functions for non-equilibrium Brownian systems. New methods yield dynamic Ornstein-Zernike equations and non-Markovian motion equations for correlators.

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Area of Science:

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

Background:

  • Classical Brownian systems are fundamental in statistical physics.
  • Understanding systems driven out of equilibrium is crucial for many physical phenomena.
  • Existing methods for deriving correlation functions can be limited.

Purpose of the Study:

  • To derive inhomogeneous two-time correlation functions for classical Brownian systems driven out of equilibrium.
  • To develop a systematic approach for constructing approximation schemes.
  • To establish non-Markovian equations of motion for two-time correlators.

Main Methods:

  • Functional differentiation of one-body density and current with respect to external fields.
  • Supplementing Smoluchowski dynamics with a vanishing source term.
  • Application of functional calculus rules.

Main Results:

  • Derivation of inhomogeneous two-time correlation functions.
  • Obtainment of a complete set of dynamic Ornstein-Zernike equations.
  • Identification of memory functions as functional derivatives of a nonlocal dissipation power functional.

Conclusions:

  • The developed techniques provide a rigorous framework for studying non-equilibrium Brownian systems.
  • The derived equations facilitate the development of novel approximation schemes.
  • The findings offer new insights into the dynamics and memory effects in complex systems.