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Published on: December 4, 2017
Nonequilibrium fluctuation-dissipation inequality and nonequilibrium uncertainty principle.
C H Fleming1, B L Hu, Albert Roura
1Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Summary
A new fluctuation-dissipation inequality for open quantum systems in nonequilibrium environments shows quantum fluctuations are bounded by quantum dissipation. This inequality aligns with the Heisenberg uncertainty principle, even at zero temperature.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Open quantum systems
Background:
- The fluctuation-dissipation relation typically applies to systems in thermal equilibrium.
- Linear response theory assumes small deviations from equilibrium.
- Temperature is not well-defined in nonequilibrium environments.
Purpose of the Study:
- To investigate fluctuation-dissipation relations in open quantum systems interacting with nonequilibrium environments.
- To establish a fluctuation-dissipation inequality beyond linear response theory.
- To explore the connection between quantum fluctuations, dissipation, and the uncertainty principle in nonequilibrium settings.
Main Methods:
- Formulation of a fluctuation-dissipation inequality for open quantum systems.
- Analysis of quantum fluctuations and dissipation in the absence of a well-defined temperature.
- Derivation of a coupling-dependent nonequilibrium fluctuation-dissipation relation.
Main Results:
- A fluctuation-dissipation inequality exists for open quantum systems in nonequilibrium environments.
- Quantum fluctuations are bounded below by quantum dissipation, unlike classical systems.
- The lower bound is satisfied by zero-temperature quantum noise, consistent with the Heisenberg uncertainty principle.
- A coupling-dependent relation determines the nonequilibrium uncertainty relation in the weak-damping limit.
Conclusions:
- The study extends the fluctuation-dissipation concept to nonequilibrium quantum systems.
- The findings reveal a fundamental link between quantum noise, dissipation, and uncertainty.
- The derived inequality provides new insights into the behavior of quantum systems interacting with their environment.
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