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Published on: August 2, 2019
Clausius inequality beyond the weak-coupling limit: the quantum Brownian oscillator
1Department of Physics, North Carolina A&T State University, Greensboro, North Carolina 27411, USA. hannibal.ikim@gmail.com
Summary
We derived an exact expression for a quantum oscillator coupled to a bath. This system behaves like a simpler oscillator at an effective temperature, confirming the second law of thermodynamics.
Area of Science:
- Quantum mechanics
- Thermodynamics
- Statistical mechanics
Background:
- The behavior of quantum systems interacting with their environment is crucial for understanding complex physical phenomena.
- Investigating quantum linear oscillators coupled to thermal baths provides insights into energy exchange and entropy under non-equilibrium conditions.
Purpose of the Study:
- To derive an exact expression for the density operator of a quantum linear oscillator coupled to a bath at arbitrary strength and temperature.
- To analyze the thermodynamic properties and validity of the second law for such a system.
Main Methods:
- Derivation of an exact closed expression for the oscillator density operator.
- Formulation of an effective Clausius inequality for the coupled system.
- Analysis of thermodynamic processes involving variations in coupling strength, mass, or spring constant.
Main Results:
- The coupled oscillator's state is noncanonical but equivalent to an uncoupled oscillator at an effective temperature, mass, and spring constant.
- An effective Clausius inequality, deltaQ*(eff) <= T*(eff)dS, was derived and confirmed.
- The second law of thermodynamics was validated for cyclic processes involving coupling strength variations.
Conclusions:
- The derived Clausius inequality is more robust than previously assumed.
- The study confirms the general validity of the second law in quantum open systems.
- The findings offer a new perspective on thermodynamic principles in quantum mechanics.
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