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Nonequilibrium Fluctuation-Response Relations: From Identities to Bounds.

Timur Aslyamov1, Krzysztof Ptaszyński2, Massimiliano Esposito1

  • 1University of Luxembourg, Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, 30 Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, Luxembourg.

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This study derives fluctuation-response relations (FRRs) for Markov jump processes, generalizing the fluctuation-dissipation theorem far from equilibrium. These relations establish new thermodynamic bounds and explain experimental observations in systems like Coulomb-blockaded devices.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Stochastic Processes

Background:

  • Markov jump processes are fundamental to modeling systems with discrete states and transitions.
  • Understanding nonequilibrium steady states is crucial for many physical and biological systems.
  • The fluctuation-dissipation theorem (FDT) relates equilibrium fluctuations to response, but its extension to nonequilibrium is challenging.

Purpose of the Study:

  • To derive exact fluctuation-response relations (FRRs) for Markov jump processes in nonequilibrium steady states.
  • To generalize the fluctuation-dissipation theorem (FDT) to systems far from equilibrium.
  • To establish and strengthen thermodynamic bounds on response and variance.

Main Methods:

  • Derivation of exact fluctuation-response relations (FRRs) for Markov jump processes.
  • Analysis of perturbations in the symmetric and antisymmetric parts of the rate matrix.
  • Application of FRRs to prove and strengthen the response thermodynamic uncertainty relation (TUR).

Main Results:

  • Exact FRRs are derived, simplifying the covariance between currents in terms of static responses.
  • FRRs imply a hierarchy of thermodynamic bounds, proving the conjectured response TUR.
  • The response TUR is strengthened using partial and pseudo-entropy production rates (EPR).
  • For antisymmetric rate perturbations, response is bounded by system traffic.

Conclusions:

  • The derived FRRs provide a powerful tool for understanding nonequilibrium systems.
  • The study establishes new fundamental thermodynamic inequalities.
  • FRRs offer an explanation for observed positive correlations in Coulomb-blockaded systems.