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Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium
Daniel Reiche1, Jen-Tsung Hsiang2, Bei-Lok Hu3
1Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße15, 12489 Berlin, Germany.
Entropy (Basel, Switzerland)
|July 27, 2022
Summary
Thermodynamic uncertainty relations (TURs) provide fundamental insights into nonequilibrium systems. This study establishes the quantum basis for TURs and extends them to the classical domain, offering improved estimates for thermodynamic uncertainties.
Area of Science:
- Quantum thermodynamics
- Statistical mechanics
- Non-equilibrium systems
Background:
- Thermodynamic uncertainty relations (TURs) are crucial for understanding thermodynamics in nonequilibrium systems.
- Previous work established the quantum basis of TURs, linking them to uncertainty principles and fluctuation-dissipation inequalities (FDI).
Purpose of the Study:
- To investigate the thermal manifestations of TURs in quantum systems.
- To extend quantum TURs to the classical domain by formulating a high-temperature thermal FDI.
- To analyze the impact of environmental back-action and bath properties on TURs.
Main Methods:
- Utilizing microphysics models of linear open quantum systems for exact solutions.
- Employing a microscopic model for bath spectral density in quantum Brownian motion.
- Deriving a thermal FDI valid at high temperatures within quantum nonequilibrium dynamics.
Main Results:
- A thermal FDI is formulated for quantum nonequilibrium dynamics, applicable at high temperatures.
- Quantum TURs are successfully bridged to the classical domain, allowing comparison with existing theories.
- Improved estimates for thermodynamic uncertainties are achieved in thermal-energy-dominated regimes.
- Exact expressions for current-current correlations of energy flux in a Brownian particle are derived.
Conclusions:
- The study provides a comprehensive quantum theoretical basis for TURs, extending to classical regimes.
- Environmental back-action and bath statistical properties are shown to be integral components of TURs.
- The derived thermal FDI offers enhanced accuracy for thermodynamic uncertainty estimations in specific regimes.
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