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Published on: May 30, 2014
Lyapounov variable: Entropy and measurement in quantum mechanics
B Misra1, I Prigogine, M Courbage
1Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium.
Summary
The second law of thermodynamics gains dynamical meaning in quantum mechanics through nonfactorizable superoperators, resolving the quantum measurement problem. This approach redefines entropy operators and their relation to time operators.
Area of Science:
- Quantum Mechanics
- Thermodynamics
- Statistical Mechanics
Background:
- Classical dynamics provides a dynamical meaning for the second law of thermodynamics using Lyapounov variables.
- Lyapounov variables require suitably unstable dynamical motion within an extended classical framework.
Purpose of the Study:
- To extend the dynamical interpretation of the second law of thermodynamics to quantum mechanics.
- To investigate the existence and properties of nonequilibrium entropy in quantum systems.
Main Methods:
- Analysis of quantum mechanics framework for defining entropy operators.
- Investigation of Hamiltonian spectral properties for entropy operator definition.
- Exploration of superoperator properties and their implications for quantum states.
Main Results:
- No standard quantum mechanical dynamical variable possesses nonequilibrium entropy characteristics.
- Entropy operators can be defined as nonfactorizable superoperators under specific Hamiltonian spectral conditions.
- Nonfactorizability of entropy operators implies loss of distinguishability between pure states and mixtures.
Conclusions:
- The study offers a solution to the quantum measurement problem by linking entropy operators to state distinguishability.
- The existence of quantum entropy operators is intrinsically connected to the definition of a time operator in quantum mechanics.
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