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Uncertainty relations for time-delayed Langevin systems.

Tan Van Vu1, Yoshihiko Hasegawa1

  • 1Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

Physical Review. E
|September 11, 2019
PubMed
Summary
This summary is machine-generated.

We reveal the thermodynamic uncertainty relation for time-delayed Langevin systems, constraining fluctuations by entropy production. This finding extends the universal trade-off between fluctuations and dissipation to non-Markovian systems.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Complex Systems

Background:

  • The thermodynamic uncertainty relation (TUR) links current fluctuations and dissipation in Markovian systems.
  • This relation has not been established for non-Markovian systems, limiting our understanding of fluctuation-dissipation theorems in complex dynamics.

Purpose of the Study:

  • To investigate and establish the thermodynamic uncertainty relation for time-delayed Langevin systems (non-Markovian systems).
  • To explore the constraints on fluctuations of dynamical observables in systems with memory effects.

Main Methods:

  • Theoretical derivation of the thermodynamic uncertainty relation for time-delayed Langevin systems.
  • Utilizing Kullback-Leibler divergence to bound path distribution differences.
  • Defining generalized entropy production for non-Markovian systems.

Main Results:

  • A generalized thermodynamic uncertainty relation is proven for arbitrary dynamical observables in time-delayed Langevin systems.
  • Fluctuations are constrained by Kullback-Leibler divergence between forward and reversed paths.
  • Lower bounds are derived for time-antisymmetric and position-odd observables, generalizing entropy production and accounting for broken symmetries.

Conclusions:

  • The derived uncertainty relations are valid for finite observation times and a broad range of time-delayed systems.
  • Numerical verification confirms the theoretical findings in single and distributed time-delay systems.
  • This work extends the applicability of thermodynamic uncertainty relations to non-Markovian dynamics.