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Fluctuation Theorem Uncertainty Relation.

Yoshihiko Hasegawa1, Tan Van Vu1

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

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This summary is machine-generated.

This study derives a new thermodynamic uncertainty relation from the fluctuation theorem. This fluctuation theorem uncertainty relation applies to various systems and observables, offering a broader understanding of nonequilibrium thermodynamics.

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Area of Science:

  • Non-equilibrium thermodynamics
  • Statistical mechanics
  • Stochastic thermodynamics

Background:

  • The fluctuation theorem is a cornerstone of non-equilibrium thermodynamics, underpinning key relations like the second law.
  • Thermodynamic uncertainty relations bound the fluctuation of observables by entropy production.

Purpose of the Study:

  • To derive a generalized thermodynamic uncertainty relation directly from the fluctuation theorem.
  • To establish the applicability of this new relation across diverse dynamical systems and observables.

Main Methods:

  • Derivation of the fluctuation theorem uncertainty relation from the established fluctuation theorem.
  • Application to overdamped Langevin dynamics with antisymmetric observables.
  • Comparison with existing uncertainty relations for continuous-time Markov chains.

Main Results:

  • A novel fluctuation theorem uncertainty relation is derived, valid for arbitrary dynamics (stochastic/deterministic) and antisymmetric observables.
  • The derived relation is shown to hold for Langevin dynamics, unlike some existing relations.
  • The relation successfully incorporates systems with time-symmetric protocols, using exerted work as the lower bound.

Conclusions:

  • The fluctuation theorem uncertainty relation provides a unified framework for thermodynamic uncertainty.
  • It offers a more general approach compared to previous relations, especially for specific system types and protocols.
  • This work expands the utility of fluctuation theorems in understanding nonequilibrium statistical mechanics.