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A generalized fluctuation-dissipation theorem (FDT) applies to nonequilibrium steady states (NESS) with temperature gradients. This allows experimental probing of long-range correlations, revealing intrinsic system rigidity beyond thermal fluctuations.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Non-equilibrium Thermodynamics

Background:

  • The fluctuation-dissipation theorem (FDT) is a cornerstone of equilibrium statistical mechanics, relating system response to equilibrium fluctuations.
  • Extending FDT to non-equilibrium systems, particularly non-equilibrium steady states (NESS), remains a significant challenge.
  • Understanding correlations and response in systems driven far from equilibrium is crucial for various fields.

Purpose of the Study:

  • To investigate the existence and nature of a generalized fluctuation-dissipation theorem (FDT) for systems in a non-equilibrium steady state (NESS).
  • To establish a framework for experimentally probing long-range correlations in such systems.
  • To elucidate the origin of these correlations, distinguishing them from thermal fluctuations.

Main Methods:

  • Theoretical analysis of a fluid in a non-equilibrium steady state (NESS) with a constant temperature gradient.
  • Derivation of a generalized FDT relating commutator correlation functions to bilinear response.
  • Identification of experimental observables and response functions for probing system properties.

Main Results:

  • A generalized FDT is demonstrated to exist for a fluid in a NESS with a temperature gradient.
  • This generalized FDT connects commutator correlation functions with the bilinear response of observable products.
  • The study reveals that observed correlations are intrinsic to the NESS and indicative of a generalized rigidity, not solely thermal fluctuations.

Conclusions:

  • The findings provide a theoretical basis for experimental investigations of non-equilibrium systems using response measurements.
  • The generalized FDT offers new insights into the fundamental properties of systems maintained in a steady state far from equilibrium.
  • The concept of generalized rigidity highlights unique characteristics of NESS beyond traditional thermodynamic descriptions.