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Dissipation, interaction, and relative entropy.

B Gaveau1, L Granger2, M Moreau3

  • 1Laboratoire analyse et physique mathématique, 14 avenue Félix Faure, F-75015 Paris, France.

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|April 16, 2014
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Summary
This summary is machine-generated.

This study reveals that the dissipative part of thermodynamic processes can be precisely quantified using relative entropy. This finding applies to both classical and quantum mechanics, linking entropy to transport coefficients.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Quantum Mechanics

Background:

  • Thermodynamic relations often involve inequalities, with equality holding only for non-dissipative processes.
  • Understanding the quantitative contribution of dissipation is crucial in various physical systems.

Purpose of the Study:

  • To derive exact equalities for thermodynamic processes that explicitly include the dissipative contribution.
  • To demonstrate the role of relative entropy (Kullback-Leibler divergence) in quantifying dissipation.

Main Methods:

  • Consideration of general time evolutions in both classical and quantum mechanics.
  • Analysis of systems with both thermal and partially thermal initial states.
  • Application of relative entropy as a measure of irreversibility.

Main Results:

  • Derivation of new thermodynamic equalities where the dissipative term is expressed using relative entropy.
  • Demonstration that relative entropy quantifies the extent of dissipation in a process.
  • Establishment of a connection between relative entropy and transport coefficients.

Conclusions:

  • Relative entropy provides a fundamental measure for dissipation in thermodynamic processes across classical and quantum regimes.
  • The derived equalities offer a new perspective on the second law of thermodynamics and irreversibility.
  • This work bridges the gap between information theory (relative entropy) and macroscopic transport phenomena.