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Related Experiment Videos

Minimal work principle: proof and counter-examples.

A E Allahverdyan1, Th M Nieuwenhuizen

  • 1Institute for Theoretical Physics, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
Summary

The minimal work principle holds for quantum systems unless energy levels cross. When level crossing occurs, optimal work processes are neither slow nor reversible, violating the principle. This study explores these quantum thermodynamics exceptions.

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Area of Science:

  • Quantum thermodynamics
  • Statistical mechanics
  • Foundations of physics

Background:

  • The minimal work principle, a formulation of the second law of thermodynamics, posits that work done on isolated systems is minimized during reversible processes.
  • This principle is crucial for understanding energy efficiency in thermodynamic processes.

Purpose of the Study:

  • To investigate the validity of the minimal work principle for finite quantum systems interacting with external work sources.
  • To identify conditions under which the minimal work principle may be violated in quantum systems.

Main Methods:

  • Theoretical analysis of finite quantum systems under external work interactions.
  • Examination of adiabatic processes and energy level behavior, specifically focusing on level crossings.

Related Experiment Videos

  • Utilizing an exactly solvable quantum model for corroboration.

    • Main Results:

    • The minimal work principle is valid for quantum systems provided their adiabatic energy levels do not cross.
    • Counter-examples demonstrate that the principle can be violated when energy level crossing occurs.
    • Optimal work processes in such cases are neither adiabatically slow nor reversible.

    Conclusions:

    • The minimal work principle's applicability in quantum thermodynamics is contingent on the absence of adiabatic energy level crossings.
    • Quantum systems exhibit unique behaviors, such as the violation of the minimal work principle, under specific conditions like level crossing.
    • Understanding these exceptions is vital for advancing the theory of quantum thermodynamics and energy manipulation.