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Dissipation: the phase-space perspective.

R Kawai1, J M R Parrondo, C Van den Broeck

  • 1Department of Physics, University of Alabama at Birmingham, Birmingham, AL 35294, USA.

Physical Review Letters
|March 16, 2007
PubMed
Summary
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This study refines the work theorem, showing average dissipation in Hamiltonian systems equals kT times the relative entropy. This provides more accurate inequalities than the second law, encompassing Landauer's principle.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Quantum Information Theory

Background:

  • The second law of thermodynamics governs energy dissipation but offers limited precision for non-equilibrium systems.
  • Understanding dissipation is crucial for fields ranging from nanoscale engines to quantum computing.

Purpose of the Study:

  • To refine the work theorem for Hamiltonian systems transitioning between equilibrium states.
  • To derive a precise formula for average dissipation in non-equilibrium processes.
  • To establish new thermodynamic inequalities that improve upon the second law.

Main Methods:

  • Refinement of the work theorem using phase-space density analysis.
  • Calculation of average dissipation using relative entropy (D(rho||rho_bar)).

Related Experiment Videos

  • Comparison of derived inequalities with the second law and Landauer's principle.
  • Main Results:

    • The average dissipation is precisely determined by = W - Delta F = kT D(rho||rho_bar).
    • The derived inequalities are more accurate than the second law for non-equilibrium systems.
    • The Landauer principle for irreversible computation is shown to be a special case of these findings.

    Conclusions:

    • The refined work theorem offers a more accurate quantitative description of energy dissipation in non-equilibrium systems.
    • This work provides a theoretical foundation for understanding and minimizing energy loss in computational processes.
    • The results have implications for the design of efficient thermodynamic devices and quantum information processing.