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Universal Upper Bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis
Akihiro Hokkyo1, Masahito Ueda1,2,3
1University of Tokyo, Department of Physics, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8654, Japan.
Physical Review Letters
|February 6, 2025
Summary
The maximum work extractable from quantum systems is limited by initial state properties and quantum operations. This finding upholds the second law of thermodynamics, even for pure quantum states, by constraining work extraction.
Area of Science:
- Quantum Thermodynamics
- Statistical Mechanics
- Condensed Matter Physics
Background:
- Quantum thermodynamics explores work extraction and energy transformations in quantum systems.
- The Eigenstate Thermalization Hypothesis (ETH) describes thermalization in isolated quantum systems.
- Understanding the interplay between thermodynamics and quantum mechanics is crucial for quantum technologies.
Purpose of the Study:
- To establish a universal upper bound on the maximum extractable work (ergotropy) from quantum many-body systems.
- To investigate the implications of this bound for work extraction from energy eigenstates.
- To connect the concepts of the second law of thermodynamics and thermalization in quantum systems.
Main Methods:
- Derivation of a universal upper bound for ergotropy based on local athermality and local entropy decrease.
- Analysis of work extraction from energy eigenstates under finite-time unitary operations.
- Investigation of the role of intrasystem correlations in quantum work extraction.
Main Results:
- The maximum extractable work is fundamentally limited by the initial state's local athermality and the entropy decrease during quantum operations.
- The Eigenstate Thermalization Hypothesis prohibits work extraction from energy eigenstates using finite-time unitary operations.
- Planck's principle, a statement of the second law of thermodynamics, is shown to hold even for pure quantum states.
Conclusions:
- Intrasystem correlations in many-body systems serve as a resource for work extraction, bridging quantum thermodynamics and thermalization.
- The study provides a unified framework for understanding work extraction limits and thermalization in quantum systems.
- The findings have implications for the fundamental understanding of energy, entropy, and work in the quantum realm.
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