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Quantum Thermodynamic Uncertainties in Nonequilibrium Systems from Robertson-Schrödinger Relations
Hang Dong1, Daniel Reiche2, Jen-Tsung Hsiang3
1State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China.
Entropy (Basel, Switzerland)
|July 27, 2022
Summary
Quantum uncertainty principles underpin thermodynamic uncertainties in nonequilibrium systems. For Gaussian systems, thermodynamic functions directly relate to the Robertson-Schrödinger uncertainty function, revealing quantum origins of these properties.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Thermodynamics
Background:
- Thermodynamic uncertainty principles provide foundational insights into nonequilibrium systems.
- Fluctuation theorems are well-established in this domain.
- Connecting thermodynamic uncertainties to quantum principles remains an open area.
Purpose of the Study:
- To trace thermodynamic uncertainties in nonequilibrium systems to their quantum origins.
- To establish a link between quantum uncertainty principles and thermodynamic functions.
- To derive new inequalities for nonequilibrium thermodynamics.
Main Methods:
- Analysis of Gaussian quantum systems.
- Derivation of thermodynamic functions from the Robertson-Schrödinger uncertainty function.
- Application of nonequilibrium free energy to derive inequalities.
- Investigation of fluctuation-dissipation relations.
Main Results:
- For Gaussian systems, thermodynamic functions are functionals of the Robertson-Schrödinger uncertainty function.
- The Robertson-Schrödinger uncertainty function is non-negative for quantum systems.
- New inequalities for nonequilibrium thermodynamics were derived, holding at all times and strong coupling.
- A fluctuation-dissipation inequality was shown to exist at all times.
Conclusions:
- This work provides a microscopic quantum basis for thermodynamic properties in macroscopic nonequilibrium systems.
- The findings establish a direct connection between quantum uncertainty and nonequilibrium thermodynamics.
- The derived inequalities offer new constraints and understanding for systems far from equilibrium.
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