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This study derives an integral relation from the Fokker-Planck equation to link steady-state probability currents with short-time relaxation dynamics. This provides a general lower bound for steady-state entropy production, offering new experimental estimation methods.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics

Background:

  • The Fokker-Planck equation describes the time evolution of probability distributions.
  • Understanding steady-state entropy production is crucial in non-equilibrium systems.
  • Relaxation dynamics provide insights into system behavior under perturbation.

Purpose of the Study:

  • To derive an integral relation connecting steady-state probability currents and short-time relaxation dynamics.
  • To establish a general lower bound for steady-state entropy production.
  • To develop feasible methods for estimating entropy production from experiments.

Main Methods:

  • Derivation of an integral relation from the Fokker-Planck equation.
  • Analysis in the limit of small perturbation fields.
  • Consideration of specific perturbation ensembles (constant gradients, density displacements).

Main Results:

  • An integral relation is established between steady-state probability currents and short-time relaxation.
  • A general lower bound on steady-state entropy production is obtained.
  • Two averaging-based thermodynamic bounds are derived for specific perturbation types.

Conclusions:

  • The derived integral relation offers a fundamental connection in non-equilibrium statistical mechanics.
  • The study provides practical, experimentally accessible bounds for entropy production.
  • This work facilitates the estimation of thermodynamic quantities from relaxation experiments.