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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Nonequilibrium detailed fluctuation theorem for repeated discrete feedback.

Jordan M Horowitz1, Suriyanarayanan Vaikuntanathan

  • 1Departamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de Madrid, 28040 Madrid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary

We generalized the detailed fluctuation theorem for thermodynamic processes with discrete feedback. This new theorem quantifies uncertainty changes from system measurements, extending key nonequilibrium work relations.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Information Theory

Background:

  • Nonequilibrium work relations are crucial for understanding energy exchange in systems driven out of equilibrium.
  • Forward and reverse processes provide a standard framework for analyzing these relations.
  • Discrete feedback introduces complexities due to information gained during the process.

Purpose of the Study:

  • To generalize the detailed fluctuation theorem for thermodynamic processes involving repeated discrete feedback.
  • To incorporate the impact of measurement-induced uncertainty into fluctuation theorems.
  • To extend existing nonequilibrium work relations, specifically the work fluctuation theorem and the relative-entropy work relation.

Main Methods:

  • Extension of the standard forward and reverse process framework.
  • Derivation of a modified detailed fluctuation theorem.
  • Inclusion of a term quantifying uncertainty change from measurements.
  • Application to specific nonequilibrium work relations.

Main Results:

  • A generalized detailed fluctuation theorem is derived for systems with discrete feedback.
  • The theorem explicitly accounts for the change in system uncertainty due to measurements.
  • The nonequilibrium work fluctuation theorem and relative-entropy work relation are successfully extended.

Conclusions:

  • The framework accommodates discrete feedback, offering a more comprehensive understanding of nonequilibrium thermodynamics.
  • Quantifying uncertainty is essential for accurate descriptions of feedback-driven processes.
  • The extended relations provide new tools for analyzing complex thermodynamic systems.