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The instantaneous fluctuation theorem.

Charlotte F Petersen1, Denis J Evans, Stephen R Williams

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Researchers derived a new instantaneous fluctuation relation for time-reversal odd phase functions. This novel relation requires observing system trajectories both before and after a specific time point, revealing non-locality in time.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Dynamical Systems

Background:

  • Fluctuation theorems are fundamental in non-equilibrium statistical mechanics.
  • Understanding transient dynamics and time-reversal symmetry is crucial.
  • Existing theorems often lack a clear form for arbitrary time-reversal odd phase functions.

Purpose of the Study:

  • To derive a new instantaneous fluctuation relation.
  • To characterize the behavior of time-reversal odd phase functions.
  • To explore the role of temporal non-locality in fluctuation theorems.

Main Methods:

  • Analytical derivation of a novel fluctuation relation.
  • Computational demonstration using a shear flow system.
  • Analysis of system trajectories in phase space.

Main Results:

  • A new instantaneous fluctuation relation was successfully derived.
  • The relation's non-obvious form necessitates observation of trajectories before and after a time point.
  • Computational results confirm the relation for various phase functions in shear flow.

Conclusions:

  • The derived relation offers new insights into non-equilibrium statistical mechanics.
  • Non-locality in time is shown to be essential for this instantaneous fluctuation theorem.
  • The findings advance the understanding of fluctuation phenomena in dynamical systems.