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Fluctuation Theorem for Many-Body Pure Quantum States.
Eiki Iyoda1, Kazuya Kaneko2, Takahiro Sagawa1
1Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
Physical Review Letters
|September 27, 2017
Summary
We demonstrate how the second law of thermodynamics emerges from quantum mechanics for pure quantum states. This finding, grounded in the Lieb-Robinson bound, links entanglement entropy to thermodynamic heat.
Area of Science:
- Quantum thermodynamics
- Statistical mechanics
- Many-body quantum systems
Background:
- The second law of thermodynamics typically applies to macroscopic systems in thermal equilibrium.
- Understanding its emergence in isolated, microscopic quantum systems is a fundamental challenge.
- The eigenstate-thermalization hypothesis (ETH) offers a potential bridge between quantum mechanics and thermodynamics.
Purpose of the Study:
- To rigorously prove the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states.
- To establish a connection between quantum entanglement and thermodynamic concepts.
- To explore the role of initial states and information propagation in quantum thermodynamics.
Main Methods:
- Mathematical derivation based on the Lieb-Robinson bound for information propagation.
- Utilizing pure quantum states with a single energy eigenstate as the initial bath state, satisfying ETH.
- Numerical simulations of hard-core bosons to validate theoretical predictions.
Main Results:
- Proof of the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states.
- Demonstration of a rigorous link between entanglement entropy of a subsystem and thermodynamic heat.
- Observation of a dynamical crossover from thermal to quantum fluctuations in simulations.
Conclusions:
- The second law of thermodynamics can emerge from fundamental quantum mechanics in isolated systems.
- Quantum entanglement plays a crucial role in the foundation of the information-thermodynamics link.
- The findings are experimentally testable using controllable quantum systems like ultracold atoms.
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