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This study extends the fluctuation-dissipation theorem to systems far from equilibrium. It establishes a new thermodynamic relation connecting arbitrary-order responses to entropy production correlations.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • The fluctuation-dissipation theorem (FDT) links equilibrium properties to responses under small perturbations.
  • Existing FDT formulations are limited to near-equilibrium or linear response regimes.

Purpose of the Study:

  • To generalize the fluctuation-dissipation theorem (FDT) for systems operating far from thermodynamic equilibrium.
  • To establish a thermodynamic relation extending FDT to arbitrary perturbation strengths.

Main Methods:

  • Derivation of a novel relation connecting higher-order responses to lower-order entropy production correlations.
  • Validation of the derived relation using a coarse-grained four-state model.

Main Results:

  • A generalized fluctuation-dissipation relation is derived, applicable beyond linear response theory.
  • The relation successfully connects arbitrary-order system responses to entropy production.
  • The derived relation is demonstrated on a non-Markovian two-state model derived from a four-state system.

Conclusions:

  • The generalized FDT provides a thermodynamic framework for understanding non-equilibrium systems.
  • This work offers a new tool for analyzing complex systems far from equilibrium.
  • The findings are relevant for statistical mechanics and thermodynamics of open systems.