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Modified Jarzynski equality in a microcanonical ensemble.

L A Williamson1

  • 1University of Queensland, ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, St Lucia, Queensland 4072, Australia.

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Summary
This summary is machine-generated.

The conventional Jarzynski equality fails for microcanonical ensembles. A modified equality is derived, linking microcanonical work fluctuations to entropy production, offering improved bounds for near-isothermal processes.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Quantum Information

Background:

  • The Jarzynski equality is a cornerstone of non-equilibrium statistical mechanics, relating equilibrium free energy differences to work done during non-equilibrium processes.
  • Conventional formulations often assume systems are prepared in a canonical ensemble, limiting applicability to systems not isolated or in thermal contact.
  • Understanding thermodynamic properties in microcanonical ensembles is crucial for isolated quantum systems and fundamental physics.

Purpose of the Study:

  • To investigate the validity of the Jarzynski equality for systems prepared in a microcanonical ensemble.
  • To derive a modified Jarzynski equality applicable to microcanonical systems.
  • To explore the relationship between work fluctuations, entropy production, and ensemble equivalence in microcanonical systems.

Main Methods:

  • Derivation of a modified Jarzynski equality for microcanonical ensembles.
  • Analysis of work fluctuations and entropy production.
  • Application of a general expression for the microcanonical moment-generating function.
  • Experimental demonstration using driven two-level spins.

Main Results:

  • The conventional Jarzynski equality does not hold for microcanonical ensembles.
  • A modified equality is derived, connecting microcanonical work fluctuations to entropy production via a path-dependent inverse temperature.
  • The modified equality provides improved bounds on average work compared to the standard free energy difference for near-isothermal processes.
  • The breakdown of ensemble equivalence for thermodynamic fluctuations can be calculated.

Conclusions:

  • The derived microcanonical Jarzynski equality extends the applicability of fluctuation theorems to isolated systems.
  • This work provides a new tool for analyzing non-equilibrium processes in microcanonical settings.
  • The findings have implications for understanding thermodynamics in quantum systems and the limits of ensemble equivalence.