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We generalized Onsager-Machlup fluctuation theory for asymmetric systems, enabling accurate analysis of hydrodynamic currents in various states. This new theory accurately predicts short-time correlations in shear flow dynamics.

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Area of Science:

  • Statistical Mechanics
  • Nonlinear Dynamics
  • Computational Physics

Background:

  • The Onsager-Machlup fluctuation theory is crucial for understanding systems with fluctuating variables.
  • Existing theories often struggle with spatially asymmetric systems and nonequilibrium steady states.
  • Accurate description of short-time correlations is vital for many physical phenomena.

Purpose of the Study:

  • To generalize the Onsager-Machlup fluctuation theory for spatially asymmetric systems.
  • To develop an analytical expression for the time autocorrelation function applicable to diverse states.
  • To validate the new theoretical framework using molecular dynamics simulations of shear flow.

Main Methods:

  • Extension of Langevin dynamics for spatially asymmetric systems.
  • Derivation of a second-order Onsager-Machlup fluctuation theory.
  • Molecular dynamics simulations of shear flow to test theoretical predictions.

Main Results:

  • A generalized Onsager-Machlup theory applicable to equilibrium and nonequilibrium steady states was derived.
  • An analytical expression for the time autocorrelation function was obtained and validated against simulations.
  • The new theory accurately captures short-time correlations, outperforming the first-order approach.

Conclusions:

  • The generalized fluctuation theory provides a robust framework for analyzing fluctuating variables in complex systems.
  • The derived time autocorrelation function accurately models computational data for shear flow.
  • The theory's utility is demonstrated via the Green-Kubo formula, revealing shear flow independence in linear nonequilibrium.