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Thermodynamic Uncertainty Relations from Exchange Fluctuation Theorems.

André M Timpanaro1, Giacomo Guarnieri2, John Goold2

  • 1Universidade Federal do ABC, 09210-580 Santo André, Brazil.

Physical Review Letters
|September 17, 2019
PubMed
Summary

We derived the tightest matrix-valued thermodynamic uncertainty relations (TURs), bounding fluctuations and correlations in quantum and classical systems. These TURs apply to general nonstationary processes and nanoscale machine design.

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Area of Science:

  • Thermodynamics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Thermodynamic uncertainty relations (TURs) bound fluctuations of thermodynamic quantities by entropy production.
  • Exchange fluctuation theorems describe heat and particle flow statistics between systems.

Purpose of the Study:

  • To identify the tightest matrix-valued TUR applicable to diverse systems and processes.
  • To extend TURs to bound correlations between thermodynamic quantities.
  • To demonstrate TURs' utility in nanoscale machine design.

Main Methods:

  • Derivation of matrix-valued TURs from exchange fluctuation theorems.
  • Analysis of heat and particle flow statistics in multi-system setups.
  • Application to quantum and classical systems under nonstationary conditions.

Main Results:

  • Identification of a tight and saturable matrix-valued TUR.
  • The TUR bounds both variances and correlations of thermodynamic quantities.
  • Demonstrated applicability to finite-time nonstationary processes in arbitrary dimensions.

Conclusions:

  • The derived TURs offer fundamental limits on thermodynamic fluctuations and correlations.
  • These findings are relevant for understanding and designing nanoscale thermodynamic engines.
  • The results provide a powerful tool for analyzing complex thermodynamic processes.